What is the solution for y^{''}-9y=sin(x)+2cos(x) ?

The solution for y^{''}-9y=sin(x)+2cos(x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/10 sin(x)-1/5 cos(x)

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y^{''}-9y=sin(x)+2cos(x)

y^{^{''}} - 9 y = sin (x) + 2 cos (x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{10} sin (x) - \frac{1}{5} cos (x)

Solution steps

y^{''} (x) - 9 y = sin (x) + 2 cos (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{10} sin (x) - \frac{1}{5} cos (x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{10} sin (x) - \frac{1}{5} cos (x)

y^{^{''}} - 5 y^{^{'}} + 6 y = (x + 1) e^{x}

y^{^{''}} - 3 y^{^{'}} + 2 y = 10

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 (x + 1)

y^{^{''}} - 6 y + 9 y = e^{- 2 x} sin (3 x)

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

What is the solution for y^{''}-9y=sin(x)+2cos(x) ?
The solution for y^{''}-9y=sin(x)+2cos(x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-1/10 sin(x)-1/5 cos(x)