What is the solution for y^{''}-2y=sin(t) ?

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

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y^{''}-2y=sin(t)

y^{^{''}} - 2 y = sin (t)

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

Solution steps

y^{''} (t) - 2 y = sin (t)

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 34 cos (2 x)

(D^{2} - 7 D + 6) y = e^{6 x} + e^{x}

\frac{d ^{2} y}{d x ^{2}} - y = 4 e^{x} cos (x)

y^{^{''}} - y^{^{'}} - 2 x = 4 x^{2}

y^{^{''}} + 2 y^{^{'}} + 4 y = 2 t - 3 cos (2 t)

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