Solution of the differential equation `x^(2)dy-2xydx=x^(3)y^(3)dx+x^(4)y^(2)dy` is

Options

A. `y=kx^(2)e^((x(2)y^(2))/2)`
B. `y=ky^(2)e^((x^(2)y^(2))/2)`
C. `y=k/(x^(2))e^((3x^(2)y^(2))/2`
D. In `(y/(x^(2)))=((xy)^(2))/4+e^(c^(2))`

Answer

A

Explanation

`(x^(2)dy-2xydx)/(x^(4))=(x^(3)y^(2)(ydx+xdy))/(x^(4))`
`(d(y/(x^(2))))/(y/(x^(2)))=xyd(xy)`
`implies` In `(y/(x^(2)))=((xy)^(2))/2+c`