What is the solution for y^{''}+2y^'=3+4sin(2x) ?

The solution for y^{''}+2y^'=3+4sin(2x) is y=c_{1}+c_{2}e^{-2x}+(3x-sin(2x)-cos(2x))/2

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y^{''}+2y^'=3+4sin(2x)

y^{^{''}} + 2 y^{^{'}} = 3 + 4 sin (2 x)

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

Solution steps

y^{''} (x) + 2 y^{'} (x) = 3 + 4 sin (2 x)

Solve linear ODE:

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

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

What is the solution for y^{''}+2y^'=3+4sin(2x) ?
The solution for y^{''}+2y^'=3+4sin(2x) is y=c_{1}+c_{2}e^{-2x}+(3x-sin(2x)-cos(2x))/2