What is the solution for y^{''}+y^'-2y=12cos(2x) ?

The solution for y^{''}+y^'-2y=12cos(2x) is y=c_{1}e^x+c_{2}e^{-2x}+3/5 sin(2x)-9/5 cos(2x)

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y^{''}+y^'-2y=12cos(2x)

y^{^{''}} + y^{^{'}} - 2 y = 12 cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{3}{5} sin (2 x) - \frac{9}{5} cos (2 x)

Solution steps

y^{''} (x) + y^{'} (x) - 2 y = 12 cos (2 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{3}{5} sin (2 x) - \frac{9}{5} cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{3}{5} sin (2 x) - \frac{9}{5} cos (2 x)

y^{^{''}} + 9 y = x e^{3 x}

(D^{2} - 3 D + 2) y = 72 x e^{- x}

y^{^{''}} + 6 y^{^{'}} + 8 = (3 x - 2) e^{4 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{- 4 t}, y (0) = 1, y (0) = 5

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

What is the solution for y^{''}+y^'-2y=12cos(2x) ?
The solution for y^{''}+y^'-2y=12cos(2x) is y=c_{1}e^x+c_{2}e^{-2x}+3/5 sin(2x)-9/5 cos(2x)