The general solution of the differential equation `y(x^(2)y+e^(x))dy=0`, is

Options

A. `x^(3)y-3e^(x)=Cy`
B. `x^(3)y+3e^(x)=3Cy`
C. `y^(3)x-3e^(y)=Cx`
D. `y^(3)x+3e^(y)=Cx`

Answer

B

Explanation

We have,
`y(x^(2)y+e^(x))dx-e^(x)dy=0`
`rArr" "x^(2)y^(2)dx+ye^(x)dx-e^(x)dy=0`
`x^(2)dx+(ye^(x)dy-e^(x)dy)/(y^(2))=0 rArrx^(2)dx+d((e^(x))/(y))=0`
On integrating, we get
`(x^(3))/(3)+(e^(x))/(y)=C rArrx^(3)y+3e^(x)=3Cy`