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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 16 y = sec (4 t)

y^{^{''}} + 4 y = 3 sin (2 x) + x^{2} - 1

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

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{2 x}

y^{^{''}} + 3 y = - 48 t^{2} e^{3 t}

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