Given the differential equation

$(\frac{x}{y^3}{e}^{\frac{x}{y}}+6x^3-\frac{1}{y^2})dx+A(x,y)dy=0$

If $\frac{y^2}{x}$ is an integrating factor, which of the following can be the solution of the differential equation?

L$$tfen birini se$$in:

A$.\frac{1}{y}{e}^{\frac{x}{y}}+2x^3{y}^2-lnx-lny=cxy$

B$.$ None of these

C$.x^2{e}^{\frac{x}{y}}-\frac{3}{2}{x}^{4}y-ylnx+y=c{y}^2$

D$.y{e}^{\frac{x}{y}}+2x^3{y}^3-ylnx+1=cy$

E$.\frac{x^2}{y^3}{e}^{\frac{x}{y}}+\frac{3}{2}{x}^4{y}^3-lnx+\frac{1}{y}=c$