Solve the differential equation `y e^(x/y)dx=(x e^(x/y)+y^2)dy(y!=0)`

Explanation

`y e^{frac{x}{y}} d x=(x e^{frac{x}{y}}+y^{2}) d y `

`rightarrow y e^{frac{x}{y}} d x=x e^{frac{x}{y}} d y+y^{2} d y `

`rightarrow y e^{frac{x}{y}} d x-x e^{frac{x}{y}} d y=y^{2} d y `

`rightarrow(y d x-x d y) e^{frac{x}{y}}=y^{2} d y`

`rightarrow frac{(y d x-x d y)}{y^{2}} e^{frac{x}{y}}=d y`

`rightarrow e^{frac{x}{y}} d(frac{x}{y})=d y `

`rightarrow int e^{frac{x}{y}} d(frac{x}{y})=int d y`

`rightarrow e^{frac{x}{y}}=y+C`