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

The solution for y^{''}+y^'=cos^2(x) is y=c_{1}+c_{2}e^{-x}+1/2 x+1/20 sin(2x)+2/5 cos(2x)-cos^2(x)

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

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

y = c_{1} + c_{2} e^{- x} + \frac{1}{2} x + \frac{1}{20} sin (2 x) + \frac{2}{5} cos (2 x) - cos^{2} (x)

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{1}{2} x + \frac{1}{20} sin (2 x) + \frac{2}{5} cos (2 x) - cos^{2} (x)

y = c_{1} + c_{2} e^{- x} + \frac{1}{2} x + \frac{1}{20} sin (2 x) + \frac{2}{5} cos (2 x) - cos^{2} (x)

y^{^{''''}} - 2 y^{^{'''}} + 2 y^{^{''}} - 2 y^{^{'}} + y = e^{x}

y^{^{''}} + 6 y^{^{'}} + 5 y = 3 e^{- x}

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

y^{^{''}} + y = 10 e^{2 x}

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 x + 1, y (0) = 1, y^{^{'}} (0) = 2

What is the solution for y^{''}+y^'=cos^2(x) ?
The solution for y^{''}+y^'=cos^2(x) is y=c_{1}+c_{2}e^{-x}+1/2 x+1/20 sin(2x)+2/5 cos(2x)-cos^2(x)