Let . Does this function satisfy the differential equation ? Justify your answer with…

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Let

y=(x^{2}+1)e^{5x}

. Does this function satisfy the differential equation

\dfrac{dy}{dx}=5(x^{2}+1)e^{5x}+2x e^{5x}

? Justify your answer with the derivative of

y