What is the solution for y^{''}-y^'-6y=2sin(t) ?

The solution for y^{''}-y^'-6y=2sin(t) is y=c_{1}e^{3t}+c_{2}e^{-2t}-7/25 sin(t)+1/25 cos(t)

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y^{''}-y^'-6y=2sin(t)

y^{^{''}} - y^{^{'}} - 6 y = 2 sin (t)

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{7}{25} sin (t) + \frac{1}{25} cos (t)

Solution steps

y^{''} (t) - y^{'} (t) - 6 y = 2 sin (t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{7}{25} sin (t) + \frac{1}{25} cos (t)

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{7}{25} sin (t) + \frac{1}{25} cos (t)

What is the solution for y^{''}-y^'-6y=2sin(t) ?
The solution for y^{''}-y^'-6y=2sin(t) is y=c_{1}e^{3t}+c_{2}e^{-2t}-7/25 sin(t)+1/25 cos(t)