What is the solution for y^{''}-4y=20t-20e^{-2t},y(0)=0,y^'(0)=12 ?

The solution for y^{''}-4y=20t-20e^{-2t},y(0)=0,y^'(0)=12 is y=3e^{2t}-3e^{-2t}-5t+5e^{-2t}t

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y^{''}-4y=20t-20e^{-2t},y(0)=0,y^'(0)=12

y^{^{''}} - 4 y = 20 t - 20 e^{- 2 t}, y (0) = 0, y^{^{'}} (0) = 12

y = 3 e^{2 t} - 3 e^{- 2 t} - 5 t + 5 e^{- 2 t} t

Solution steps

y^{''} (t) - 4 y = 20 t - 20 e^{- 2 t}

Solve linear ODE:

y = 3 e^{2 t} - 3 e^{- 2 t} - 5 t + 5 e^{- 2 t} t

y = 3 e^{2 t} - 3 e^{- 2 t} - 5 t + 5 e^{- 2 t} t

What is the solution for y^{''}-4y=20t-20e^{-2t},y(0)=0,y^'(0)=12 ?
The solution for y^{''}-4y=20t-20e^{-2t},y(0)=0,y^'(0)=12 is y=3e^{2t}-3e^{-2t}-5t+5e^{-2t}t