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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 cosh (x)

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x sin^{2} (x)

(d^{3} - 6 d^{2} + 11 d - 6) y = e - 2 x + e - 3 x

(d^{2} + 4) y = sin^{3} (x)

(d - 4) y = x^{2}

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