What is the solution for y^{''}-4y=4x^{(2)}e^{(2)}x ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y = e^{x} cos (x), y (0) = 1, y^{^{'}} (0) = 2

y^{^{'''}} + 6 y^{^{''}} + 12 y^{^{'}} + 8 y = 5 e^{- 2 x}

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 10 y = e^{2 x} + 20

y^{^{''}} - 2 y^{^{'}} - 35 y = - 97 t + 70 t^{2}

y^{^{'''}} + y^{^{''}} = 7 x^{2}

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