What is the solution for y^{''}-4y^'+4y=2e^{2x}+4x-12 ?

The solution for y^{''}-4y^'+4y=2e^{2x}+4x-12 is y=c_{1}e^{2x}+c_{2}xe^{2x}+e^{2x}x^2+x-2

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y^{''}-4y^'+4y=2e^{2x}+4x-12

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 e^{2 x} + 4 x - 12

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

Solution steps

y^{''} (x) - 4 y^{'} (x) + 4 y = 2 e^{2 x} + 4 x - 12

Solve linear ODE:

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

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

y^{^{''}} + y - 5 = e^{2 x} - 3 + cos (3 x)

y^{^{''}} - 4 y = 2 e^{3 x}

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

y^{^{''}} + 2 y^{^{'}} + 4 y = 3 sin (5 t)

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 cos (x)

What is the solution for y^{''}-4y^'+4y=2e^{2x}+4x-12 ?
The solution for y^{''}-4y^'+4y=2e^{2x}+4x-12 is y=c_{1}e^{2x}+c_{2}xe^{2x}+e^{2x}x^2+x-2