Question in orthogonal trajectories

[manal950]

Hi

answer b

I forget first step

2aydy/dx = 3x^2


please can check my answer

 

[haruspex]

I'm not able to follow the logic of your method, but it does not seem to give a valid answer. The original family is g(x, y) = x³/y² = a; if your answer f(x, y) = y²+x = c is correct then you should find ∇f.∇g = 0. ∇g = (3x²/y², -2x³/y³); ∇f = (1, 2y); ∇f.∇g = 3x²/y² - 4x³/y².