Telegram group: T.me/BBCNOUN ====== MTH232 ====== 1. For a homogeneous equation \(a(x,y)dy+b(x,y)dx=0\), when \(bx+ay\neq 0\), then ____ is an integrating factor \(bx+ay=0\) \(\frac{1}{bx-ay}\) \(bx-ay=0\) --->> \(\frac{1}{bx+ay}\) 2. An exact differential equation is formed by equating an exact differential to ____ 2 3 1 --->> \(0\) 3. 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 \(f(x,y)\) --->> \(\frac{dy}{dx}=f(x,y)\) \(f(x,y)=0\) \(\frac{dy}{dx}=-f(x,y)\) 4. In order to solve \((x^4 e^x-2my^2 x)dx+2mx^2 ydy=0\), the integrating factor is _____ \(bx+ay=-1\) \(\frac{1}{bx+ay}\) \(bx+ay=0\) --->> \(frac{1}{x^4}\) 5. The expression \(a(x,y)dy+b(x,y)dx is an_________ partial differential equation --->> exact differential equation elementary differential equation ordinary differential equation 6. A factor, which when multiplied with a non-exact differential equation make it exact, is known as an ____ factor determinant --->> integrating factor integration 7. 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 \(bx+ay=0\) \(\frac{1}{bx-ay}\) \(bx-ay=0\) --->> \(\frac{1}{bx+ay}\) 8. A differential equation \(\frac{dy}{dx}=f(x,y)\) is called a _____ when f is homogeneous function of degree zero. exact differential equation elementary differential equation --->> Homogenous differential equation partial differential equation 9. Solving \(x \frac{dy}{dx}+y=x^3\) the answer can be _______ \(-x-y=\frac{x^4}{4}+c\) \(-xy=-\frac{x^4}{4}+c\) --->> \(-xy=\frac{x^4}{4}+c\) \(-xy=\frac{x^4}{4}-c\) 10. Let \(Y_i\) be a particular solution of \(\fraac{dy}{dx}+P_i (x)y=Q_1 (x)\) where \(Q_1 (x)\) are continuous functions defined on an interval for I=1,2,…n, then the function _____ defined on I is a particular solution of \(\frac{dy}{dx}+P_i (x)y=Q_1 (x)\) --->> \(y_p=y_1+y_2+…+y_n\) \(y_p=-y_1+y_2+…+y_n\) \(y_p=y_1-y_2+…+y_n\) \(-y_p=y_1+y_2+…+y_n\)