The solution of the differential equation
`y(2x^(4)+y)(dy)/(dx) = (1-4xy^(2))x^(2)` is given by

Options

A. `3(x^(2)y^(2))^(2)+y^(3)-x^(3)=c`
B. `xy^(2)+y^(3)/3-x^(3)/3+c=0`
C. `2/5yx^(5)+y^(3)/3=x^(3)/3-(4xy^(3))/3+c`
D. None of these

Answer

A

Explanation

`y(2x^(4)+y)(dy)/(dx) =(1-4xy^(2))x^(2)`
or `2x^(4)ydy+y^(2)dy+4x^(3)y^(2)dx-x^(2)dx=0`
or `2x^(2)y(x^(2)dy+2xydx) +y^(2)dy-x^(2)dx=0`
or `2x^(2)yd(x^(2)y)+y^(2)dy-x^(2)dx=0`
Integrating, we get `(x^(2)y)^(2)+y^(3)/3-x^(3)/3=c`
or `3(x^(2)y)^(2)+y^(3)-x^(3)=c`