The solution of the diffferential equation
` x (dy)/(dx ) + 2y = x^(2) ` is

Options

A. ` y = (x^(2)+C)/(4x^(2))`
B. `y = (x^(2))/4+C`
C. `y= (x^(4)+C)/(x^(2))`
D. ` y = (x^(4)+C)/(4x^(2))`

Answer

b

Explanation

Given , `(dy)/(dx) +2/x y = x `
This is linear differential equation
` :. " Integrating factor " =e^(int 2/x dx) = x^(2) `
` :. "Required solution is "`
` y * x^(@) = int x^(3) dx + C/4 = (x^(4))/4 +C/4 `
` rArr y = (x^(4)+C)/(4x^(2))`