What is the solution for y^{''}-6y^'+5y=34sin(3t) ?

The solution for y^{''}-6y^'+5y=34sin(3t) is y=c_{1}e^{5t}+c_{2}e^t-2/5 sin(3t)+9/5 cos(3t)

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y^{''}-6y^'+5y=34sin(3t)

y^{^{''}} - 6 y^{^{'}} + 5 y = 34 sin (3 t)

y = c_{1} e^{5 t} + c_{2} e^{t} - \frac{2}{5} sin (3 t) + \frac{9}{5} cos (3 t)

Solution steps

y^{''} (t) - 6 y^{'} (t) + 5 y = 34 sin (3 t)

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{t} - \frac{2}{5} sin (3 t) + \frac{9}{5} cos (3 t)

y = c_{1} e^{5 t} + c_{2} e^{t} - \frac{2}{5} sin (3 t) + \frac{9}{5} cos (3 t)

y^{^{''}} - 9 y^{^{'}} + 2 y = t e^{t}

y^{^{''}} + 4 y = 8 sin (2 t) + 5 e^{t}

y^{^{''}} - 8 y^{^{'}} + 16 y = 45 e^{7 t}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} = 6 x^{2} + 2 x - 2

y^{^{''}} - 8 y^{^{'}} + 16 y = 2 e^{4 x}

What is the solution for y^{''}-6y^'+5y=34sin(3t) ?
The solution for y^{''}-6y^'+5y=34sin(3t) is y=c_{1}e^{5t}+c_{2}e^t-2/5 sin(3t)+9/5 cos(3t)