`y = x^3` Determine whether the function is a solution of the differential equation `xy'

Saturday, April 20, 2013

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.

$\displaystyle{y}'={3}{{x}}^{{2}}$

Now we plug the into the equation.

$\displaystyle{x}\cdot{3}{{x}}^{{2}}-{2}\cdot{{x}}^{{3}}={3}{{x}}^{{3}}-{2}{{x}}^{{3}}={{x}}^{{3}}\ne{{x}}^{{3}}{{e}}^{{x}}$

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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