What is the solution for (d^2-4)y=x^2e^3x ?

The solution for (d^2-4)y=x^2e^3x is y=c_{1}e^{2x}+c_{2}e^{-2x}-(e^3x^3)/4-(3e^3x)/8

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(d^2-4)y=x^2e^3x

(d^{2} - 4) y = x^{2} e^{3} x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{e ^{3} x ^{3}}{4} - \frac{3 e ^{3} x}{8}

Solution steps

(d^{2} - 4) y = x^{2} e^{3} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{e ^{3} x ^{3}}{4} - \frac{3 e ^{3} x}{8}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{e ^{3} x ^{3}}{4} - \frac{3 e ^{3} x}{8}

What is the solution for (d^2-4)y=x^2e^3x ?
The solution for (d^2-4)y=x^2e^3x is y=c_{1}e^{2x}+c_{2}e^{-2x}-(e^3x^3)/4-(3e^3x)/8