Vinod Singh and Shweta Pawar Solutions for Chapter: Differential Equations, Exercise 2: Critical Thinking

An integrating factor of the differential equation $\left(1-x^2\right)\frac{dy}{dx}-xy=1$ is

An integrating factor of the differential equation $x\frac{dy}{dx}+y\log x=x{\mathrm{e}}^x{x}^{-\frac{1}{2}\log x}, \left(x>0\right)$ is

An integrating factor of the differential equation $\left(1+y^2\right)dx-\left({\tan }^{-1}y-x\right)dy=0$ is

The solution of the differential equation $\frac{dy}{dx}+2y\cot x=3x^2{cosec}^{2}x$ is

The solution of $\frac{dy}{dx}+2y\tan x=\sin x$ is

The solution of the equation $\frac{dy}{dx}=\frac{1}{x+y+1}$ is

The solution of the differential equation $x\frac{dy}{dx}+y=x^2+3x+2$ is

The solution of the differential equation $x\log x\frac{dy}{dx}+y=2\log x$ is