What is the solution for (d+4)y=x^2cos^2(x) ?

The solution for (d+4)y=x^2cos^2(x) is y=c_{1}e^{-4x}+e^{-4x}*integral of e^{4x}x^2cos^2(x)

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(d+4)y=x^2cos^2(x)

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

y = c_{1} e^{- 4 x} + e^{- 4 x} \cdot \int e^{4 x} x^{2} cos^{2} (x) d x

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 4 x} + e^{- 4 x} \cdot \int e^{4 x} x^{2} cos^{2} (x) d x

y = c_{1} e^{- 4 x} + e^{- 4 x} \cdot \int e^{4 x} x^{2} cos^{2} (x) d x

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

(d^{2} - 4 d - 12) \cdot y = (x - 1) \cdot e^{2 x}

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

(d^{2} - 6 d + 9) y = 2 e^{3 x}

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

What is the solution for (d+4)y=x^2cos^2(x) ?
The solution for (d+4)y=x^2cos^2(x) is y=c_{1}e^{-4x}+e^{-4x}*integral of e^{4x}x^2cos^2(x)