What is the solution for y^{''}-90y=sin(2x) ?

The solution for y^{''}-90y=sin(2x) is y=c_{1}e^{3sqrt(10)x}+c_{2}e^{-3sqrt(10)x}-1/94 sin(2x)

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y^{''}-90y=sin(2x)

y^{^{''}} - 90 y = sin (2 x)

y = c_{1} e^{310 x} + c_{2} e^{- 310 x} - \frac{1}{94} sin (2 x)

Solution steps

y^{''} (x) - 90 y = sin (2 x)

Solve linear ODE:

y = c_{1} e^{310 x} + c_{2} e^{- 310 x} - \frac{1}{94} sin (2 x)

y = c_{1} e^{310 x} + c_{2} e^{- 310 x} - \frac{1}{94} sin (2 x)

y^{^{''}} + 25 \cdot y = \frac{1}{sin ( 5 \cdot x )}

y^{^{''}} + y = 3 sin (2 x) + 5 x cos (2 x)

- 6 y^{^{''}} + 5 y^{^{'}} - 1 y = 1 t^{2} - 1 t + 6 e^{2} t

y^{^{''}} + 4 y^{^{'}} + 29 y = 200 sin (x)

\frac{d ^{2} y}{d x ^{2}} + 2 y = 6 x, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}-90y=sin(2x) ?
The solution for y^{''}-90y=sin(2x) is y=c_{1}e^{3sqrt(10)x}+c_{2}e^{-3sqrt(10)x}-1/94 sin(2x)