What is the solution for y^{''}-4y=4t-4 ?

The solution for y^{''}-4y=4t-4 is y=c_{1}e^{2t}+c_{2}e^{-2t}-t+1

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y^{''}-4y=4t-4

y^{^{''}} - 4 y = 4 t - 4

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

Solution steps

y^{''} (t) - 4 y = 4 t - 4

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = 6

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - 1 = 0

y^{^{''}} + 9 y = 6 cot (3 t) cos (3 t)

2 y^{^{''}} - 3 y^{^{'}} = 9 x^{2} + 10, y (0) = 1, y^{^{'}} (0) = - 3

x^{^{''}} + 2 x^{^{'}} + x = 3 cos (t)

What is the solution for y^{''}-4y=4t-4 ?
The solution for y^{''}-4y=4t-4 is y=c_{1}e^{2t}+c_{2}e^{-2t}-t+1