What is the solution for 9y^{''}-16y=sin(x) ?

The solution for 9y^{''}-16y=sin(x) is y=c_{1}e^{(4x)/3}+c_{2}e^{-(4x)/3}-1/25 sin(x)

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9y^{''}-16y=sin(x)

9 y^{^{''}} - 16 y = sin (x)

y = c_{1} e^{\frac{4 x}{3}} + c_{2} e^{- \frac{4 x}{3}} - \frac{1}{25} sin (x)

Solution steps

9 y^{''} (x) - 16 y = sin (x)

Solve linear ODE:

y = c_{1} e^{\frac{4 x}{3}} + c_{2} e^{- \frac{4 x}{3}} - \frac{1}{25} sin (x)

y = c_{1} e^{\frac{4 x}{3}} + c_{2} e^{- \frac{4 x}{3}} - \frac{1}{25} sin (x)

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

y^{^{''}} + 25 y = 3, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 20 y^{^{'}} + 200 y = 400

y^{^{'''}} - 7 y^{^{''}} = x^{2} + 2 cos (x)

y^{^{''}} + y = tan^{2} (t)

What is the solution for 9y^{''}-16y=sin(x) ?
The solution for 9y^{''}-16y=sin(x) is y=c_{1}e^{(4x)/3}+c_{2}e^{-(4x)/3}-1/25 sin(x)