What is the solution for 9y^{''}-4y=sin(x) ?

The solution for 9y^{''}-4y=sin(x) is y=c_{1}e^{(2x)/3}+c_{2}e^{-(2x)/3}-1/13 sin(x)

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9y^{''}-4y=sin(x)

9 y^{^{''}} - 4 y = sin (x)

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

Solution steps

9 y^{''} (x) - 4 y = sin (x)

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} - 4 y = 2 sin (x)

\frac{d ^{2} y}{d x ^{2}} + y = cos (x)

y^{^{''''}} + 2 y^{^{''}} + y = 3 + cos (2 t)

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

y^{^{''}} + 3 y^{^{'}} + 2 y = cos (t) - sin (2 t)

What is the solution for 9y^{''}-4y=sin(x) ?
The solution for 9y^{''}-4y=sin(x) is y=c_{1}e^{(2x)/3}+c_{2}e^{-(2x)/3}-1/13 sin(x)