MTH232

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1.	.........is an example of nonlinear differential equation.
	Answer: \\((x+y)^2\\frac{dy}{dx}=1\\)

2.	A differential equation \(\\frac{dy}{dx}=f(x,y)\) is called a .............when f is homogeneous function of degree zero.
	Answer: homogenous differential equation

3.	A solution of a differential equation which cannot be obtained by assigning definite values to the arbitrary constraints in the general solution is called its.............
	Answer: singular solution

5.	The sufficient conditions for existence of solution of the first order equation \(\\frac{dy} {dx}=f(x,y)\), with 
	\(y(x_0 )=y_0\) in a region T defined by\( |x-x_0 |<a\) and \(|y-y_0 |<b\) are _
	ANSWER: f is continuous in t and f is bounded in t

6.	Solving \(x \\frac{dy}{dx}+y=x^3\) the answer can be
	Answer: \\(-xy=\\frac{x^4}{4}+c\\)

7.	The problem of doing a differential equation together with initial conditions is called the....
	Answer: initial value problem

8.	For a homogeneous equation \ (a(x,y)dy+b(x,y)dx=0\), when \(bx+ay\\neq 0\), then is an integrating factor
	Answer: \\(\\frac{1}{bx+ay}\\)

9.	An equation of the form \(\\frac{dy} {dx}=f(x,y)\) is called a ........
	Answer: separable equation

10.	The coefficients of a......... are either constant or functions of the independent variable or variables-
	Answer: linear equation

11.	is an ordinary linear differential equafion.
	Answer: \\(\\frac{d^2y}{dx^2}+y=x^2\\)

12.	Given that \(bx+ay\\neq 0\) and the differential equation \(a(x,y)dy+b(x,y)dx=0\) an be written in the form \(yf,(x,y)dx+xf_2 (x,y)dy=0\), then....... is an integrating factor
	Answer: \\(\\frac{1}{bx+ay}\\)

13.	An equation of the form ................is called equation in variable separable form if\ (f(x,y)\) can be put in the form \ (f(x,y)=X(x)Y(y)\) where X and Y are given functions of x and y respectively
	Answer: \\(\\frac{dy}{dx}=f(x,y)\\)

14.	Any solution which is obtained from the general solution by giving particular values to the arbitrary constraint is called a...........
	Answer: particular solution

15.	An exact differential equation is formed by equating an exact differential to.........
	Answer: \\(0\\)

16.	Conditions on the value of the dependent variable, and its derivatives, at a single value of the independent variable in the interval of existence of the solution are called the.........
	Answer: initial conditions.

17.	Afactor, which when multiplied with a non-exact differential equation make it exact, is known as an...........
	Answer: integrating factor

18.	In order to solve \((x^4 e^x—2my^2 x)dx+2mx^2 ydy=0\), the integrating factor is
	Answer: \\(frac{1}{x^4}\\)

19.	The expression \(a(x,y)dy+b(x,y)dx is an.......
	Answer: exact differential equation

20.	

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