What is the solution for y^{''}+2y^'-8y=-650sin(3t) ?

The solution for y^{''}+2y^'-8y=-650sin(3t) is y=c_{1}e^{2t}+c_{2}e^{-4t}+34sin(3t)+12cos(3t)

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y^{''}+2y^'-8y=-650sin(3t)

y^{^{''}} + 2 y^{^{'}} - 8 y = - 650 sin (3 t)

y = c_{1} e^{2 t} + c_{2} e^{- 4 t} + 34 sin (3 t) + 12 cos (3 t)

Solution steps

y^{''} (t) + 2 y^{'} (t) - 8 y = - 650 sin (3 t)

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 4 t} + 34 sin (3 t) + 12 cos (3 t)

y = c_{1} e^{2 t} + c_{2} e^{- 4 t} + 34 sin (3 t) + 12 cos (3 t)

What is the solution for y^{''}+2y^'-8y=-650sin(3t) ?
The solution for y^{''}+2y^'-8y=-650sin(3t) is y=c_{1}e^{2t}+c_{2}e^{-4t}+34sin(3t)+12cos(3t)