What is the solution for y^{''}-4y=sin(x) ?

The solution for y^{''}-4y=sin(x) is y=c_{1}e^{2x}+c_{2}e^{-2x}-1/5 sin(x)

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y^{''}-4y=sin(x)

y^{^{''}} - 4 y = sin (x)

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

Solution steps

y^{''} (x) - 4 y = sin (x)

Solve linear ODE:

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

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

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

4 y^{^{''}} + 2 y^{^{'}} + 70 y = 4 cos (4 t)

y^{^{''''}} - 2 y^{^{''}} - 8 y = 6 e^{2 x}

y^{^{''}} - 5 y^{^{'}} + 6 y = π x^{2} + 3

y^{^{'''}} + y^{^{''}} = 9 x^{2}

What is the solution for y^{''}-4y=sin(x) ?
The solution for y^{''}-4y=sin(x) is y=c_{1}e^{2x}+c_{2}e^{-2x}-1/5 sin(x)