What is the solution for y^{''}-4y^'+4y=4(x+1) ?

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

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y^{''}-4y^'+4y=4(x+1)

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 (x + 1)

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

Solution steps

y^{''} (x) - 4 y^{'} (x) + 4 y = 4 (x + 1)

Solve linear ODE:

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

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

y^{^{''}} - 6 y + 9 y = e^{- 2 x} sin (3 x)

y^{^{''}} - y^{^{'}} + 2 y = 3 sin (3 x)

y^{^{''''}} + 2 y^{^{''}} + y = 9 t + 6

y^{^{''''}} + 2 y^{^{''}} + y = 9 t + 2

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

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