What is the solution for -y^{''}+y^'+2y=72t+400sin(t)+36 ?

The solution for -y^{''}+y^'+2y=72t+400sin(t)+36 is y=c_{1}e^{-t}+c_{2}e^{2t}+36t+120sin(t)-40cos(t)

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-y^{''}+y^'+2y=72t+400sin(t)+36

- y^{^{''}} + y^{^{'}} + 2 y = 72 t + 400 sin (t) + 36

y = c_{1} e^{- t} + c_{2} e^{2 t} + 36 t + 120 sin (t) - 40 cos (t)

Solution steps

- y^{''} (t) + y^{'} (t) + 2 y = 72 t + 400 sin (t) + 36

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{2 t} + 36 t + 120 sin (t) - 40 cos (t)

y = c_{1} e^{- t} + c_{2} e^{2 t} + 36 t + 120 sin (t) - 40 cos (t)

What is the solution for -y^{''}+y^'+2y=72t+400sin(t)+36 ?
The solution for -y^{''}+y^'+2y=72t+400sin(t)+36 is y=c_{1}e^{-t}+c_{2}e^{2t}+36t+120sin(t)-40cos(t)