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

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

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

linear

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^{^{'''}} + y^{^{'}} - 10 y = 29 e^{4 x}

f^{^{''}} (x) + 3 f^{^{'}} (x) + 2 f (x) = 2, f (0) = 3, f^{^{'}} (0) = 5

y^{^{''}} - 6 y^{^{'}} + 10 y = 180 sin (2 x)

y^{^{''}} - 9 y^{^{'}} + 20 y = e^{x} (- 9 - 78 x + 36 x^{2})

y^{^{''}} - 3 y^{^{'}} - 10 y = - 18 t + 20 t^{2}

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