What is the solution for y^{''}-4y=4x-4 ?

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

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y^{''}-4y=4x-4

y^{^{''}} - 4 y = 4 x - 4

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} = 8 x^{3}

y^{^{''}} + 6 y^{^{'}} + 8 y = 4 t^{2} - 3 t + 2

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

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} = 6 t

y^{^{''}} + 9 y = 9 cos^{3} (3 x)

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