Question Number 100684 by bemath last updated on 28/Jun/20

(x^2 +xy) (dy/dx) = xy + y^2

Answered by bobhans last updated on 28/Jun/20

set y = sx ⇒ (dy/dx) = s + x (ds/dx) (x^2 +x^2 s) (s +x (ds/dx)) = x^2 s + x^2 s^2 (1+s) (s + x (ds/dx)) = s(s+1) s + x (ds/dx) = s ⇒ x (ds/dx) = 0 (ds/dx) = 0 ⇒ s = 0+C ; (y/x) = C , x ≠ 0 y = Cx