Find the differential equation of the given family
Y^ 3 = C X^2 + 3 .
The answer in the packet is y' - 2y = -4e^(-2x).
( but i have no idea how to get it) Thanks

Question

Find the differential equation of the given family 
Y^ 3  = C X^2 + 3 . 
The answer in the packet is y'  - 2y = -4e^(-2x).
 ( but i have no idea how to get it) Thanks

unklerhaukus · Answer

take the laplace transform of both sides

anonymous · Answer

Multiply both sides of the differential equation by $e^{−2x}.$ Then the left side becomes a perfect derivative, and you can now solve by integrating both sides. You will find that the solution you gave in your original post is not the correct one.