Question

Solve:$\frac{dy}{dx}+x\frac{y}{x}=\frac{y^2}{x^2}$

Answer 1

Given,

$\frac{dy}{dx}+x\frac{y}{x}=\frac{y^2}{x^2}$

$\frac{dy}{dx}+y=\frac{y^2}{x^2}$

$\frac{dy}{dx}+Py=Q$

$P=1,Q=\frac{y^2}{x^2}$

$I.F=e^{\int Pdx}$

$=e^{\int 1dx}$

$=e^x$

$y\times I.F=\int Q\times I.F\times dx+c$

$y\times e^x=\int \frac{y^2}{x^2}\times e^{x}dx$

$y{e}^x=y^2(-\frac{e^x}{x}+\text{Ei}\left(x\right))+C$