The solution of the differential equation `(xy^4 + y) dx-x dy = 0,` is

Answer

`3x^(4)y^(3)+4x^(3)=cy^(3)`

Explanation

The given equation is `xy^(4)dx+ydx-xdy=0`
Dividing by `y^(4)`, we get
`xdx+(ydx-xdy)/y^(4)=0`……………..(1)
or `x^(3)dx+(x/y)^(2)d(x//y)=0`………….(2)
Integrating equation (2), we get `x^(4)/4+1/3(x/y)^(3)=c`
or `3x^(4)y^(3)+4x^(3)=cy^(3)`, which is the required solution.