What is the solution for y^{''}+y^'-12y=sin(t) ?

The solution for y^{''}+y^'-12y=sin(t) is y=c_{1}e^{3t}+c_{2}e^{-4t}-13/170 sin(t)-1/170 cos(t)

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y^{''}+y^'-12y=sin(t)

y^{^{''}} + y^{^{'}} - 12 y = sin (t)

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{13}{170} sin (t) - \frac{1}{170} cos (t)

Solution steps

y^{''} (t) + y^{'} (t) - 12 y = sin (t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{13}{170} sin (t) - \frac{1}{170} cos (t)

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{13}{170} sin (t) - \frac{1}{170} cos (t)

y^{^{''}} - y^{^{'}} - 6 y = 250 t e^{- 2 t}

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2}

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

y^{^{''}} - 8 y^{^{'}} + 16 y = \frac{e ^{4 x}}{x}

(2 D^{2} - 3 D + 1) y = csc (2 π x)

What is the solution for y^{''}+y^'-12y=sin(t) ?
The solution for y^{''}+y^'-12y=sin(t) is y=c_{1}e^{3t}+c_{2}e^{-4t}-13/170 sin(t)-1/170 cos(t)