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

Options

A. ` e^(2y) +e^(3x) +x^(3) +C`
B. ` 1/2 e^(2y) =1/3 (e^(3x)+x^(3))+C`
C. ` 1/2 e^(2y) = 1/3 (e^(3x)+x^(3))+C `
D. ` e ^(2y)= e^(3x) + x^(2) +C`

Answer

d

Explanation

Given differential equation can be rewritten as ,
` e^(2y)dy = (e^(3x)+x^(2))dx`
On integrating , we get
` rArr (e^(2y))/2 = (e^(3x))/3 +x^(3)/3 + C`