What is the solution for y^{''}+y^'-12y=2cos(t) ?

The solution for y^{''}+y^'-12y=2cos(t) is y=c_{1}e^{3t}+c_{2}e^{-4t}+1/85 sin(t)-13/85 cos(t)

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y^{''}+y^'-12y=2cos(t)

y^{^{''}} + y^{^{'}} - 12 y = 2 cos (t)

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{1}{85} sin (t) - \frac{13}{85} cos (t)

Solution steps

y^{''} (t) + y^{'} (t) - 12 y = 2 cos (t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{1}{85} sin (t) - \frac{13}{85} cos (t)

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{1}{85} sin (t) - \frac{13}{85} cos (t)

D^{2} (D - 1) y = 8 e^{2 x}

x^{^{''}} - x^{^{'}} - 6 x = 2 e^{4 t}

y^{^{''}} + a y = b

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

y^{^{''}} + 25 y = 3 x, y (0) = 1, y^{^{'}} (0) = 5

What is the solution for y^{''}+y^'-12y=2cos(t) ?
The solution for y^{''}+y^'-12y=2cos(t) is y=c_{1}e^{3t}+c_{2}e^{-4t}+1/85 sin(t)-13/85 cos(t)