What is the solution for y^{''}+4y=16t ?

The solution for y^{''}+4y=16t is y=c_{1}cos(2t)+c_{2}sin(2t)+4t

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y^{''}+4y=16t

y^{^{''}} + 4 y = 16 t

y = c_{1} cos (2 t) + c_{2} sin (2 t) + 4 t

Solution steps

y^{''} (t) + 4 y = 16 t

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + 4 t

y = c_{1} cos (2 t) + c_{2} sin (2 t) + 4 t

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{4 t} ln (t)

10 y^{^{''}} + 1000 y = 100 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y^{^{'}} + 14 y = 2 + t, y (0) = 1, y^{^{'}} (0) = 1

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 9 e^{- t} + 3

y^{^{''}} + 10 y^{^{'}} + 25 y = 14 \cdot e^{- 5 x}

What is the solution for y^{''}+4y=16t ?
The solution for y^{''}+4y=16t is y=c_{1}cos(2t)+c_{2}sin(2t)+4t