The solution of the differential equation: $x \cos y d y=\left(x e^x \log x+e^x\right) d x$ is

The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$, when $y(1)=2$ is :

Find the function ' $f$ ' which satisfies the equation $\frac{d f}{d x}=2 f$, given that $f(0)=e^3$

Solve the following differential equation $\cos ^2 x \frac{d y}{d x}+y=\tan x$, given that $y(0)=1$. Hence find $y\left(\frac{\pi}{4}\right)$