What is the solution for y^{''}+y-2y=2t-40cos(2t) ?

The solution for y^{''}+y-2y=2t-40cos(2t) is y=c_{1}e^t+c_{2}e^{-t}-2t+8cos(2t)

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y^{''}+y-2y=2t-40cos(2t)

y^{^{''}} + y - 2 y = 2 t - 40 cos (2 t)

y = c_{1} e^{t} + c_{2} e^{- t} - 2 t + 8 cos (2 t)

Solution steps

y^{''} (t) + y - 2 y = 2 t - 40 cos (2 t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} - 2 t + 8 cos (2 t)

y = c_{1} e^{t} + c_{2} e^{- t} - 2 t + 8 cos (2 t)

What is the solution for y^{''}+y-2y=2t-40cos(2t) ?
The solution for y^{''}+y-2y=2t-40cos(2t) is y=c_{1}e^t+c_{2}e^{-t}-2t+8cos(2t)