What is the solution for y^{''}-4y^'+4y=2(9x-2)e^{2x} ?

The solution for y^{''}-4y^'+4y=2(9x-2)e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+3x^3e^{2x}-2e^{2x}x^2

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y^{''}-4y^'+4y=2(9x-2)e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 (9 x - 2) e^{2 x}

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

Solution steps

y^{''} (x) - 4 y^{'} (x) + 4 y = 2 (9 x - 2) e^{2 x}

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 10 cos (5 x) + 15 sin (5 x)

y^{^{''}} - 7 y^{^{'}} + 12 y = x^{2} e^{x}

y^{^{''}} - y^{^{'}} - 20 y = 72 e^{2 t}

y^{^{''}} - y = t, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 2 y + 5 = 0

What is the solution for y^{''}-4y^'+4y=2(9x-2)e^{2x} ?
The solution for y^{''}-4y^'+4y=2(9x-2)e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+3x^3e^{2x}-2e^{2x}x^2