What is the solution for y^{''}+5y^'=29sin(-2t) ?

The solution for y^{''}+5y^'=29sin(-2t) is y=c_{1}+c_{2}e^{-5t}+sin(2t)+5/2 cos(2t)

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y^{''}+5y^'=29sin(-2t)

y^{^{''}} + 5 y^{^{'}} = 29 sin (- 2 t)

y = c_{1} + c_{2} e^{- 5 t} + sin (2 t) + \frac{5}{2} cos (2 t)

Solution steps

y^{''} (t) + 5 y^{'} (t) = 29 sin (- 2 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 t} + sin (2 t) + \frac{5}{2} cos (2 t)

y = c_{1} + c_{2} e^{- 5 t} + sin (2 t) + \frac{5}{2} cos (2 t)

What is the solution for y^{''}+5y^'=29sin(-2t) ?
The solution for y^{''}+5y^'=29sin(-2t) is y=c_{1}+c_{2}e^{-5t}+sin(2t)+5/2 cos(2t)