The general solution of $$\frac{d y}{d x}=\frac{x+y}{x-y}$$ is

The particular solution of the diffrential equation $$y(1+\log x)=\left(\log x^x\right) \frac{d y}{d x}$$, when $$y(e)=e^2$$ is

The general solution of $$\sin ^{-1}\left(\frac{d y}{d x}\right)=x+y$$ is

Solution of the differential equation $$\mathrm{y'=\frac{(x^2+y^2)}{xy}}$$, where y(1) = $$-$$2 is given by