$~29.~~x\left(\frac{dy}{dx}+y\right)=1-y$ Sol. $~~~x\left(\frac{dy}{dx}+y\right)=1-y \\ \Rightarrow \frac{dy}{dx}+y=\…

$~22.~~(1+x)~\frac{dy}{dx}-xy=1-x$ Sol. $~~~~~(1+x)~\frac{dy}{dx}-xy=1-x \\ \Rightarrow \frac{dy}{dx}-\frac{x}{1+x}~y=\…

$~15.~~\frac{dy}{dx}+\frac{2x}{1+x^2}y=\frac{1}{(1+x^2)^2}$ Sol. $~~~\frac{dy}{dx}+\frac{2x}{1+x^2}y=\frac{1}{(1+x^2)…

$~8.~~4~\frac{dy}{dx}+8y=5e^{-3x}$ Sol. $~~4~\frac{dy}{dx}+8y=5e^{-3x} \\ \therefore \frac{dy}{dx}+2y=\frac 54 e^{-3x…

Solve: $~1.~~\frac{dy}{dx}-\frac{2}{x+1}y=(x+1)^3$ Sol. $~~~\frac{dy}{dx}-\frac{2}{x+1}y=(x+1)^3\rightarrow(1)$ and it …