` (1 + x^(2)) (dy)/(dx) + 2xy = 4x ^(2)`, given that `y = 0`, when `x =0`

Options

A. `3x(1+y^(2)) = 4y^(3) +C`
B. `3y (1+x^(2))= 4x^(3)+C`
C. `3x(1-y^(2)) = 4y^(3) +C`
D. ` 3y(1+y^(2))=4x^(3) +C`

Answer

b

Explanation

Given , `(dy)/(dx) + (2y)/(1+x^(2)) * y = (4x^(2))/(1+x^(2))`
` :. IF = e^(int (2x)/(1+x^(2))dx) = e^(log (1+x^(2))) = (1_+x^(2))`
` :. ` General solution is
` y * (1+x^(2)) = int (1+x^(2))* (4x^(2))/(1+x^(2))dx`
` rArr y (1+x^(2)) = (4x^(3))/3 +C_(1)`
` rArr 3y (1+x^(2)) = 4x^(3) +C " " [ :' C = 3C_(1)]`