The solution of the differential equation d y d x = y ^ (x)-y^2 (x) is

Step-by-step solution

aligned & d y d x = y ^ (x)-y^2 (x) = y ^ (x) (x) - y^2 (x) & d y d x = y^2 ^ (x) y (x) - y^2 (x) aligned aligned & 1 y^2 ( d y d x )= ^ (x) y (x) - 1 (x) & 1 y^2 ( d y d x )- 1 y ^ (x) (x) = -1 (x) aligned Let t = -1 y dt dx = 1 y ^2 ( dy dx ) dt dx + t ^ ( x ) ( x ) = -1 ( x ) I . F=e^ ^ (x) (x) d x =e^ (x) = (x) Solution of differential equation is aligned t ( x ) & = -1 ( x ) ( x ) dx -1 y ( x ) & =- x - c ( x ) y = x + c y = ( x ) x + c aligned