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

The solution for y^{''}-4y^'+4y=x^{-4}*e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+(e^{2x})/(6x^2)

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y^{''}-4y^'+4y=x^{-4}*e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{- 4} \cdot e^{2 x}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x}}{6 x ^{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x}}{6 x ^{2}}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x}}{6 x ^{2}}

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2} + 3 + 2 cos (2 x)

2 y^{^{''}} - 3 y^{^{'}} + y = 64

y^{^{''}} - 3 y + 2 = x^{2} + 2 x + 1

y^{^{''}} - y^{^{'}} = x^{2} + 1

5 y^{^{''}} + 7 y^{^{'}} + 3 y = x^{2} + 2 e^{5 x}

What is the solution for y^{''}-4y^'+4y=x^{-4}*e^{2x} ?
The solution for y^{''}-4y^'+4y=x^{-4}*e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+(e^{2x})/(6x^2)