What is the solution for (D^2-4)y=cos^2(x) ?

The solution for (D^2-4)y=cos^2(x) is y=c_{1}e^{2x}+c_{2}e^{-2x}+(cos(2x)-4cos^2(x))/(16)

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(D^2-4)y=cos^2(x)

(D^{2} - 4) y = cos^{2} (x)

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{cos ( 2 x ) - 4 cos ^{2} ( x )}{16}

Solution steps

(D^{2} - 4) y = cos^{2} (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{cos ( 2 x ) - 4 cos ^{2} ( x )}{16}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{cos ( 2 x ) - 4 cos ^{2} ( x )}{16}

What is the solution for (D^2-4)y=cos^2(x) ?
The solution for (D^2-4)y=cos^2(x) is y=c_{1}e^{2x}+c_{2}e^{-2x}+(cos(2x)-4cos^2(x))/(16)