What is the solution for y^{''}-9y=sin(t)-cos(t) ?

The solution for y^{''}-9y=sin(t)-cos(t) is y=c_{1}e^{3t}+c_{2}e^{-3t}-1/10 sin(t)+1/10 cos(t)

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y^{''}-9y=sin(t)-cos(t)

y^{^{''}} - 9 y = sin (t) - cos (t)

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

Solution steps

y^{''} (t) - 9 y = sin (t) - cos (t)

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 6 x + 6 e^{- x}

2 y^{^{''}} + 4 y^{^{'}} + 2 y = sin (2 x) + 2 x cos (2 x)

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

y^{^{''}} - 5 y^{^{'}} - 6 y = x e - 5 x

\frac{5}{2} x^{^{''}} + 10 x^{^{'}} + 20 x = 200, x (0) = 0

What is the solution for y^{''}-9y=sin(t)-cos(t) ?
The solution for y^{''}-9y=sin(t)-cos(t) is y=c_{1}e^{3t}+c_{2}e^{-3t}-1/10 sin(t)+1/10 cos(t)