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

The solution for y^{''}+y^'-2y=-sin(2x) is y=c_{1}e^x+c_{2}e^{-2x}+3/20 sin(2x)+1/20 cos(2x)

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

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{3}{20} sin (2 x) + \frac{1}{20} cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{3}{20} sin (2 x) + \frac{1}{20} cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{3}{20} sin (2 x) + \frac{1}{20} cos (2 x)

What is the solution for y^{''}+y^'-2y=-sin(2x) ?
The solution for y^{''}+y^'-2y=-sin(2x) is y=c_{1}e^x+c_{2}e^{-2x}+3/20 sin(2x)+1/20 cos(2x)