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

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

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

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

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{1}{4} sin (2 x) - \frac{1}{4} cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{1}{4} sin (2 x) - \frac{1}{4} cos (2 x)

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{1}{4} sin (2 x) - \frac{1}{4} cos (2 x)

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