What is the solution for (d^2-1)y=sin^2(x) ?

The solution for (d^2-1)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^2-1)y=sin^2(x)

(d^{2} - 1) y = sin^{2} (x)

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

Solution steps

(d^{2} - 1) 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)

41 H (x) - 8 u^{^{'}} + u^{^{''}} = 0

y^{^{''}} - 3 y = 6 x

y^{^{''}} + y = e^{t} sin (t), y (0) = 0, y^{^{'}} (0) = 0

\frac{1}{2} y^{^{''}} + 5 y^{^{'}} + 12 y = e^{- 4 x} (4 x - 2)

2 y^{^{''}} + 5 y^{^{'}} + 2 y = x^{3} + 9 e^{4 x}

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