What is the solution for y^{''}=2y^'+15y+sin(3t) ?

The solution for y^{''}=2y^'+15y+sin(3t) is y=c_{1}e^{5t}+c_{2}e^{-3t}-2/51 sin(3t)+1/102 cos(3t)

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y^{''}=2y^'+15y+sin(3t)

y^{^{''}} = 2 y^{^{'}} + 15 y + sin (3 t)

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{2}{51} sin (3 t) + \frac{1}{102} cos (3 t)

Solution steps

y^{''} (t) = 2 y^{'} (t) + 15 y + sin (3 t)

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{2}{51} sin (3 t) + \frac{1}{102} cos (3 t)

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{2}{51} sin (3 t) + \frac{1}{102} cos (3 t)

What is the solution for y^{''}=2y^'+15y+sin(3t) ?
The solution for y^{''}=2y^'+15y+sin(3t) is y=c_{1}e^{5t}+c_{2}e^{-3t}-2/51 sin(3t)+1/102 cos(3t)