What is the solution for y^{''}-4y=4t-4,y(0)=2,y^'(0)=9 ?

The solution for y^{''}-4y=4t-4,y(0)=2,y^'(0)=9 is y=3e^{2t}-2e^{-2t}-t+1

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y^{''}-4y=4t-4,y(0)=2,y^'(0)=9

y^{^{''}} - 4 y = 4 t - 4, y (0) = 2, y^{^{'}} (0) = 9

y = 3 e^{2 t} - 2 e^{- 2 t} - t + 1

Solution steps

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

Solve linear ODE:

y = 3 e^{2 t} - 2 e^{- 2 t} - t + 1

y = 3 e^{2 t} - 2 e^{- 2 t} - t + 1

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

y^{^{''}} + 4 y = x cos (x)

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

y^{^{''}} + y^{^{'}} - 6 y = 6 x^{3} - 3 x^{2} + 12 x

y^{^{''}} + 6 y^{^{'}} + 12 y = 763 e^{2 t} cos (7 t)

What is the solution for y^{''}-4y=4t-4,y(0)=2,y^'(0)=9 ?
The solution for y^{''}-4y=4t-4,y(0)=2,y^'(0)=9 is y=3e^{2t}-2e^{-2t}-t+1