What is the solution for y^{''}-16y=16t-32e^{-4t},y(0)=0,y^'(0)=51 ?

The solution for y^{''}-16y=16t-32e^{-4t},y(0)=0,y^'(0)=51 is y=6e^{4t}-6e^{-4t}-t+4e^{-4t}t

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y^{''}-16y=16t-32e^{-4t},y(0)=0,y^'(0)=51

y^{^{''}} - 16 y = 16 t - 32 e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 51

y = 6 e^{4 t} - 6 e^{- 4 t} - t + 4 e^{- 4 t} t

Solution steps

y^{''} (t) - 16 y = 16 t - 32 e^{- 4 t}

Solve linear ODE:

y = 6 e^{4 t} - 6 e^{- 4 t} - t + 4 e^{- 4 t} t

y = 6 e^{4 t} - 6 e^{- 4 t} - t + 4 e^{- 4 t} t

What is the solution for y^{''}-16y=16t-32e^{-4t},y(0)=0,y^'(0)=51 ?
The solution for y^{''}-16y=16t-32e^{-4t},y(0)=0,y^'(0)=51 is y=6e^{4t}-6e^{-4t}-t+4e^{-4t}t