Solution of the differential equation `dy/dx=(y^3)/(e^(2x)+y^2)` , is

Options

A. `e^(-2x) y^(2) + 2In|y|= c`
B. `e^(2x)y^(2)=2In|y| = c`
C. `e^(x)+In|y| = c`
D. None of these

Answer

A

Explanation

`(dy)/(dx)=(y^(3))/(e^(2x)+y^(2))`
Dividing by `e^(2x)`
`therefore" "(dy)/(dx)=(y^(3)e^(-2x))/(1+y^(2)e^(-2x))`
`therefore" "dy + y^(2)e^(-2x)dy = y^(3)e^(-2x)dx`
`therefore" "int 2 (dy)/(y) + int 2 (ye^(-2x)dy - y^(2)e^(-2x)dx)= 0`
`therefore" "int 2 (dy)/(y)+ int d(e^(-2x)y^(2))+c=0`
`therefore" "2 "In"|y| + e^(-2x) y^(2) = c`