Calculus of a Single Variable, Chapter 6, 6.1, Section 6.1, Problem 22

In order to check if the given function is solution of th given differential equation, we first need to find the derivative of the function.
y'=3x^2
Now we plug the into the equation.
x cdot 3x^2-2cdotx^3=3x^3-2x^3=x^3 ne x^3e^x
Since the left and the right hand side of the equation are not equal, the given function is not a solution to the given differential equation.