What is the solution for (d^2y)/(dx^2)-y=sin^2(x) ?

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

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(d^2y)/(dx^2)-y=sin^2(x)

\frac{d ^{2} y}{d x ^{2}} - y = sin^{2} (x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = sin^{2} (x)

Solve linear ODE:

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

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

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