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.
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