FBQ1: The theory of differential equations involves the interplay of ____________ and their derivatives.
Answer: *Function*
FBQ2: An equation involving one (or more) dependent variable derivatives with respect to one or more ------------------- variables is called a differential equation.
Answer: *Independent*
FBQ3: dydx=2y-2x2+3 is an example of ____________ differential equation
Answer: *Ordinary*
FBQ4: Isaac Newton was able to model the motion of a particle by an equation involving an unknown function and one or more of its____________
Answer: *Derivative*
FBQ5: Given a function of two variables z=fx, y; ∂z∂x is the ____________ partial derivative of z with respect to x and it is obtained by differentiating z with respec
Answer: *first order*
FBQ6: Given a function of two variables z=fx, y; ∂z∂y is the first order partial derivative of z with respect to y and it is obtained by differentiating z with respect
Answer: *X*
FBQ7: Differential equations are divided into three classes, namely; ordinary, partial and ____________
Answer: *Total*
FBQ8: The order of a differential equation is the order of the ____________ order derivative appearing in the equation.
Answer: *Highest*
FBQ9: The degree of a differential equation is the highest -------------- of the highest order derivative appearing in it after the equation has been expressed in the form free from radicals and any fractional power of the derivatives or negative power.
Answer: *Exponent*
FBQ10: The equation x-ydydx2=r21+dydx<
Answer: *Three*
FBQ11: The equation ∂2z∂x2+∂2z∂y2-∂</mo&g
Answer: *Partial*
FBQ12: The equation dydx=ex+y is a good example of ____________ equation.
Answer: *Separable*
FBQ13: The equation dydx=exy is ____________ a separable equation.
Answer: *not*
FBQ14: The equation dydx=ex+y ____________ a separable equation.
Answer: *Is*
FBQ15: hx, y=x3+2x2y+3xy2+4y3 is ____________ of degree
Answer: *Homogeneous*
FBQ16: A differential equation y'=fx,y is called a homogeneous differential equation when f is a homogeneous ____________ of degree 0
Answer: *Function*
FBQ17: An exact differential equation is formed by equating an exact differential to ____________
Answer: *Zero*
FBQ18: A factor, which when multiplied with a non-exact differential equation makes it ____________ , is known as an integrating factor.
Answer: *Exact*
FBQ19: A differential equation is ____________ if the dependent variable and all its derivatives appear only in the first degree and also there is no term involving the product of the derivatives or any derivative and the dependent variable.
Answer: *Linear*
FBQ20: A differential equation is linear if the ____________ variable and all its derivatives appear only in the first degree and also there is no term involving the product of the derivatives or any derivative and the dependent variable.
Answer: *Dependent*
FBQ21: Given that dydx+Pxy=Qx is the general form of the linear equation of the first order, where Px and Qx</
Answer: *non-homogeneous*
FBQ22: Given that dydx+Pxy=Qx is the general form of the linear equation of the first order, where Px and Qx</
Answer: *Homogeneous*
FBQ23: Fx,y,c=x+y+c=0 represents a family of ____________ straight lines; each line corresponds to precisely one value of the parameter c
Answer: *Parallel*
FBQ24: Fx,y,c=x2+y2+c2=0 represents a family of concentric ____________ of radius c with centre at the origin.
Answer: *Circles*
FBQ25: A set of functions y1x,y2x, …,ynx defined on an interval I is linearly ___________
Answer: *Dependent*
FBQ26: Method of undetermined coefficients is applicable if the equation is a ____________ equation with constant coefficients
Answer: *Linear*
FBQ27: Method of undetermined coefficients is applicable if the ____________ term is either a polynomial, an exponential function, a sinusoidal function or a product of these functions
Answer: *non-homogeneous*
FBQ28: If we know one solution of the homogeneous linear differential equation of the second order, we can solve the non-homogeneous equation by the method of ____________ and obtain both a particular solution and a second linearly independent solution of the homogeneous equation.
Answer: *reduction of order*
FBQ29: If we know one solution of the homogeneous linear differential equation of the second order, we can solve the non-homogeneous equation by the method of reduction of order and obtain both a particular solution and a second linearly independent solution of the ____________ equation.
Answer: *Homogeneous*
FBQ30: The differential equation x3d3ydx3+x2d2ydx<
Answer: *Euler's*
FBQ31: The three classes of differential equation are; ordinary, total and ____________
Answer: *Partial*
FBQ32: Given y2∂z∂x+xy∂z∂x=nzx; ∂z∂x is a ____________ derivative of <math xmlns="h
Answer: *Partial*
FBQ33: Given y2∂z∂x+xy∂z∂x=nzx; ∂z∂y is a partial derivative of <math xmlns="http:/
Answer: *X*
FBQ34: The partial derivatives of a function of two variables z=fx, y with respect to one of the ____________ variables x, can be defined as ∂z∂x=∂f∂x
Answer: *Independent*
FBQ35: The partial derivatives of a function of two variables z=fx, y with respect to one of the independent variables ____________ can be defined as ∂z∂x=∂f∂x.
Answer: *X*
FBQ36: Given a function of two variables z=fx, y; ∂z∂x is the first order partial derivative of z with respect to x and it is obtained by differentiating z with respect
Answer: *Constant*
FBQ37: The most obvious classification of differential equations is based on the ____________ of the dependent variable and its derivative (or derivatives) in the equation.
Answer: *Nature*
FBQ38: The most obvious classification of differential equations is based on the nature of the dependent ____________ and its derivative(or derivatives) in the equation.
Answer: *Variable*
FBQ39: ____________ differential equation is the equation involving only derivatives (that is , derivatives with respect to a single independent variable)
Answer: *Ordinary*
FBQ40: If y=fx is a given function then its derivation dydx can be interpreted as the rate of change of ____________ with respect to x
Answer: *Y*
FBQ41: The primary purpose of differential equations is to serve as a tool for studying ____________ in the physical world
Answer: *Change*
FBQ42: Sir Isaac Newton observed that certain important laws of natural sciences can be phrased in terms of ____________ involving rates of change.
Answer: *Equations*
FBQ43: ____________ differential equation is the equation containing partial derivatives of one ( or more) dependent variable with respect to two or more independent variable.
Answer: *Partial*
FBQ44: Partial differential equation is the equation containing partial derivatives of one ( or more) dependent variable with respect to two or more ____________ variable.
Answer: *Independent*
FBQ45: The ____________ of a differential equation is the order of the highest order derivative appearing in the equation.
Answer: *Order*
FBQ46: The differential equation d2ydx2+y=x2 is of ____________ order
Answer: *Two*
FBQ47: The equation x-ydydx2=r21+dydx<
Answer: *Four*
FBQ48: The equation, x+y2dydx=1 , is a/an ____________ non-linear equation.
Answer: *Ordinary*
FBQ49: The equation ∂2z∂x2+∂2z∂y2-∂</mo&g
Answer: *Partial*
FBQ50: In differential equation, a particular solution is any solution which is obtained from the ____________ by giving particular values to the arbitrary constants.
Answer: *general solution*
Multiple Choice Questions (MCQs):
MCQ1: If y=fx is a given function then its derivation dydx can be interpreted as the rate of change of ----------- with respect to x
Answer: f
MCQ2: The primary purpose of differential equations is to serve as a tool for studying -------in the physical world
Answer: change
MCQ3: Sir Isaac Newton observed that certain important laws of natural sciences can be phrased in terms of -------involving rates of change.
Answer: equations
MCQ4: Isaac Newton was able to model the motion of a particle by an equation involving an unknown function and one or more of its------
Answer: directions
MCQ5: The theory of differential equations involves the interplay of ------- and their derivatives.
Answer: derivatives
MCQ6: An equation involving one (or more) dependent variable derivatives with respect to one or more independent variables is called a -------------------
Answer: simultaneous equation
MCQ7: dydx=2y-2x2+3 is an example of ---------------differential equation
Answer: partial
MCQ8: Given y2∂z∂x+xy∂z∂x=nzx; ∂z∂x is a --------- derivative of <math xmlns="http
Answer: differential
MCQ9: Given y2∂z∂x+xy∂z∂x=nzx; ∂z∂y is a partial derivative of <math xmlns="http:/
Answer: x
MCQ10: The partial derivatives of a function of two variables z=fx, y with respect to one of the independent variables x, can be defined as ------------
Answer: ∂x∂y=∂y∂x
MCQ11: Given a function of two variables z=fx, y; ∂z∂x is the first order partial derivative of z with respect to x and it is obtained by differentiating z with respect
Answer: constant
MCQ12: If z=fx, y is a function of two variables, then ∂z∂y is the first order partial derivative of z with respect to y and it is obtained by differentiating z with r
Answer: f
MCQ13: The most obvious classification of differential equations is based on the nature of the ----------------- variable and its derivative(or derivatives) in the equation.
Answer: independent
MCQ14: A differential equation involving only derivatives ( that is , derivatives with respect to a single independent variable) is called an ---------------------- differential equation.
Answer: partial
MCQ15: Differential equation containing partial derivatives of one ( or more) dependent variable with respect to two or more independent variable is called a ------------- differential equation.
Answer: total
MCQ16: The ------------ of a differential equation is the order of the highest order derivative appearing in the equation.
Answer: power
MCQ17: The differential equation d2ydx2+y=x2 is of ----------- order
Answer: Zero
MCQ18: The equation, x+ydydx2=1 is of ---------- order
Answer: Zero
MCQ19: The ----------------- of a differential equation is the highest exponent of the highest order derivative appearing in it after the equation has been expressed in the form free from radicals and any fractional power of the derivatives or negative power.
Answer: Power
MCQ20: The equation x-ydydx2=r21+dydx<
Answer: Three
MCQ21: When in an ordinary or partial differential equation, the dependent variables and its derivatives occur to the degree only, and not as higher powers or products, we call the equation -----------
Answer: Non-linear
MCQ22: The differential equation d2ydx2+y=x2 is an ordinary ----------differential equation.
Answer: non-linear
MCQ23: The equation, x+y2dydx=1 , is an ordinary ---------- equation
Answer: non-linear
MCQ24: The equation ∂2z∂x2+∂2z∂y2-∂</mo&g
Answer: non-exact
MCQ25: The solution of the nth order differential equation with arbitrary 'n' constants is called its ---------solution.
Answer: particular
MCQ26: In differential equation, any solution which is obtained from the general solution by giving particular values to the arbitrary constants is called a ------------- solution.
Answer: particular
MCQ27: The general solution of a first order differential equation normally contains one arbitrary constant which is called a ------------------
Answer: constant
MCQ28: Y=mx+c is a -----parameter family of cueves
Answer: one
MCQ29: Which of the following does not indicate situation(s) where differential equations occur naturally --------------------
Answer: solving differential equation
MCQ30: Conditions on the value of the dependent variable, and its derivative, at a single value of the independent variable in the interval of existence of the solution are called the -----------------
Answer: general conditions
MCQ31: The problem of solving a differential equation together with the initial conditions is called the ----------------------
Answer: general condition
MCQ32: The general solution of a -------------- differential equation represents one-parameter family of curves.
Answer: second order
MCQ33: The general solution of a nth order differential equation represents -------------- family of curves.
Answer: nm-parameter
MCQ34: Many physical situation such as population mode, Newton's law of cooling, radioactive decay, can be represented by ------- differential equations
Answer: second order
MCQ35: An equation of the form dydx=fx, y is called a ---------- if fx, y can be put in the form fx, y<
Answer: separable equation
MCQ36: An equation of the form dydx=fx, y is called equation in variable separable form if fx, y can be put in the form ----------- where X and <mi&
Answer: fx, y=XYy
MCQ37: A real-value function hx, y of two variables x and y is called a -------------------function of degree n, where n is a real number, if we have hλx, <
Answer: homogeneous
MCQ38: The function hx, y=x3+2x2y+3xy2+4y3 is homogeneou
Answer: three
MCQ39: A differential equation y'=fx,y is called a homogeneous differential equation when f is a homogeneous function of ----------------------------------
Answer: degree 1
MCQ40: An exact differential ----------- is formed by equating an exact differential to zero
Answer: inequality
MCQ41: A factor, which when multiplied with a non-exact differential equation makes it exact, is known as an --------------factor.
Answer: exact
MCQ42: A differential equation is ------------------ if the dependent variable and all its derivatives appear only in the first degree and also there is no term involving the product of the derivatives or any derivative and the dependent variable.
Answer: non-linear
MCQ43: --------- differential equations can be applied in population model, radioactive decay and Newton's law of cooling.
Answer: non-linear
MCQ44: Given that dydx+Pxy=Qx is the general form of the linear equation of the first order, where Px and Qx</
Answer: homogeneous
MCQ45: Given that dydx+Pxy=Qx is the general form of the linear equation of the first order, where Px and Qx</
Answer: homogeneous
MCQ46: px+px+py+xy=0 is equivalent to ------------
Answer: p-xp+y=0.
MCQ47: Fx,y,c=x+y+c=0 represents a family of ----------- lines; each line corresponds to precisely one value of the parameter c
Answer: parallel circles
MCQ48: Fx,y,c=x2+y2+c2=0 represents a family of ---------- of radius c with centre at the origin.
Answer: parallel circles
MCQ49: A set of functions y1x,y2x, …,ynx defined on an interval I is ---------------if fo
Answer: linearly non-homogeneous
MCQ50: Method of undetermined coefficients is applicable if the equation is a ----------- equation with constant coefficients
Answer: non-linear