What is the solution for 25y^{''}-9y=sin(x) ?

The solution for 25y^{''}-9y=sin(x) is y=c_{1}e^{(3x)/5}+c_{2}e^{-(3x)/5}-1/34 sin(x)

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25y^{''}-9y=sin(x)

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

y = c_{1} e^{\frac{3 x}{5}} + c_{2} e^{- \frac{3 x}{5}} - \frac{1}{34} sin (x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{3 x}{5}} + c_{2} e^{- \frac{3 x}{5}} - \frac{1}{34} sin (x)

y = c_{1} e^{\frac{3 x}{5}} + c_{2} e^{- \frac{3 x}{5}} - \frac{1}{34} sin (x)

y^{^{''}} + 2 y^{^{'}} - 24 y = 6 x

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

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

y^{^{''}} + y = sec (x) csc (x)

y^{^{'''}} + 3 y^{^{''}} - 4 y = e^{- 2 x}

What is the solution for 25y^{''}-9y=sin(x) ?
The solution for 25y^{''}-9y=sin(x) is y=c_{1}e^{(3x)/5}+c_{2}e^{-(3x)/5}-1/34 sin(x)