What is the solution for y^{''}+y^'-2y=2+5cos(2x) ?

The solution for y^{''}+y^'-2y=2+5cos(2x) is y=c_{1}e^x+c_{2}e^{-2x}+(sin(2x)-3cos(2x))/4-1

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y^{''}+y^'-2y=2+5cos(2x)

y^{^{''}} + y^{^{'}} - 2 y = 2 + 5 cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{sin ( 2 x ) - 3 cos ( 2 x )}{4} - 1

Solution steps

y^{''} (x) + y^{'} (x) - 2 y = 2 + 5 cos (2 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{sin ( 2 x ) - 3 cos ( 2 x )}{4} - 1

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{sin ( 2 x ) - 3 cos ( 2 x )}{4} - 1

What is the solution for y^{''}+y^'-2y=2+5cos(2x) ?
The solution for y^{''}+y^'-2y=2+5cos(2x) is y=c_{1}e^x+c_{2}e^{-2x}+(sin(2x)-3cos(2x))/4-1