What is the solution for y^{''}-9y=sin(2t) ?

The solution for y^{''}-9y=sin(2t) is y=c_{1}e^{3t}+c_{2}e^{-3t}-1/13 sin(2t)

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y^{''}-9y=sin(2t)

y^{^{''}} - 9 y = sin (2 t)

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{13} sin (2 t)

Solution steps

y^{''} (t) - 9 y = sin (2 t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{13} sin (2 t)

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{13} sin (2 t)

\int_{7}^{9} (x^{2} + 2 x - 2) d x

\frac{d}{d x} ((3)^{x})

\int \frac{2 x + 1}{4 x ^{2} + 4 x + 7} d x

f (x) = 3 sin (x)

F (r) = \frac{2}{r ^{3}}

What is the solution for y^{''}-9y=sin(2t) ?
The solution for y^{''}-9y=sin(2t) is y=c_{1}e^{3t}+c_{2}e^{-3t}-1/13 sin(2t)