What is the solution for y^{''}-5y^'+6y=-sin(5t) ?

The solution for y^{''}-5y^'+6y=-sin(5t) is y=c_{1}e^{3t}+c_{2}e^{2t}+19/986 sin(5t)-25/986 cos(5t)

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y^{''}-5y^'+6y=-sin(5t)

y^{^{''}} - 5 y^{^{'}} + 6 y = - sin (5 t)

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{19}{986} sin (5 t) - \frac{25}{986} cos (5 t)

Solution steps

y^{''} (t) - 5 y^{'} (t) + 6 y = - sin (5 t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{19}{986} sin (5 t) - \frac{25}{986} cos (5 t)

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{19}{986} sin (5 t) - \frac{25}{986} cos (5 t)

What is the solution for y^{''}-5y^'+6y=-sin(5t) ?
The solution for y^{''}-5y^'+6y=-sin(5t) is y=c_{1}e^{3t}+c_{2}e^{2t}+19/986 sin(5t)-25/986 cos(5t)