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

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

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(d^2-1)y=x^2+cos^2(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

(d^{2} + d - 6) y = e^{2} x \cdot sin^{3} (x)

y^{^{''}} + y^{^{'}} - 6 y = 6 x^{2} - 2 x - 2

y^{^{''}} + 4 y = x^{23} e^{x}

(d^{2} - 4 d + 4) \cdot y = x^{3}

(d^{3} - 25 d) y = sin^{2} (x) cos^{2} (x)

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