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

The solution for y^{''}+y^'=sin(2x) is y=c_{1}+c_{2}e^{-x}-1/5 sin(2x)-1/10 cos(2x)

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

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

y = c_{1} + c_{2} e^{- x} - \frac{1}{5} sin (2 x) - \frac{1}{10} cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} - \frac{1}{5} sin (2 x) - \frac{1}{10} cos (2 x)

y = c_{1} + c_{2} e^{- x} - \frac{1}{5} sin (2 x) - \frac{1}{10} cos (2 x)

What is the solution for y^{''}+y^'=sin(2x) ?
The solution for y^{''}+y^'=sin(2x) is y=c_{1}+c_{2}e^{-x}-1/5 sin(2x)-1/10 cos(2x)