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)

y^{^{''}} - 6 y^{^{'}} + 8 y = - 2 e^{2 t}

y^{^{''}} - 2 y^{^{'}} - 17 y = sin (t) - cos (t)

y^{^{''}} + 4 y = 3 cos (a x)

y^{^{''}} - 3 y^{^{'}} - 4 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = - 1

(d^{2} - 2 d + 5) y = e^{- x}

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)