The solution of differential equation `(dy)/(dx) + xy = xy^(2)` is

Options

A. ` y = 1+Ce^(x^(2)//2)`
B. ` 1/y = 1+Ce^(x^(2)//2)`
C. ` 1/y = 1+ Ce^(x//2)`
D. None of these

Answer

b

Explanation

On dividing by `y^(2)` on both sides of given equATION , WE GET ltbr gt ` y^(-2) (dy)/(dx) +1/y x = x`
Let ` 1/y = z rArr =1/(y^(2)) (dy)/(dx) = (dz)/(dx)`
Then , given equation reduces to
` (dz)/(dx) - xz = - x`
` :. IF = e^(int -xdx) = e^(-x^(2)//2)`
The solution is
` ze^(-x^(2)//2) = int (-x)*e ^(-x^(2)//x) dx + C = e^(-x^(2)//2) dx + C = e^(-x^(2)//2) +C`
i.e ` 1/y = 1+ Ce^(x^(2)//2)`