Show that the differential equation of which y = 2(x^2 - 1) + ce^(-x^2) is a solution,

Question

Show that the differential equation of which y = \(2\left(x^2 - 1 \right) + ce^{-x^2}\) is a solution, is \(\frac{dy}{dx}+2xy = 4x^3.\)

Answer 1

y = \(2\left(x^2 - 1 \right) + ce^{-x^2}\)

On differentiating with respect to x we have,

Which is the given equation.

Hence,  y = \(2\left(x^2 - 1 \right) + ce^{-x^2}\) is solution to the given differential equation.