What is the solution for d^2(d^2+4)y=96x^2+sin^2(x)-k ?

The solution for d^2(d^2+4)y=96x^2+sin^2(x)-k is

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d^2(d^2+4)y=96x^2+sin^2(x)-k

d^{2} (d^{2} + 4) y = 96 x^{2} + sin^{2} (x) - k

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{256 x ^{4} - 16 k x ^{2} + 8 x ^{2} - 768 x ^{2} cos ^{2} ( 2 x ) - 768 x ^{2} sin ^{2} ( 2 x ) + 4 x sin ( 2 x ) + 8 k cos ^{2} ( 2 x ) + 8 k sin ^{2} ( 2 x ) + 4 cos ( 2 x ) + 384 cos ^{2} ( 2 x ) + 8 sin ^{4} ( x ) cos ( 2 x ) + 384 sin ^{2} ( 2 x ) - 16 sin ^{3} ( x ) sin ( 2 x ) cos ( x ) - sin ( 2 x ) sin ( 4 x )}{128}

Solution steps

d^{2} (d^{2} + 4) y = 96 x^{2} + sin^{2} (x) - k

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{256 x ^{4} - 16 k x ^{2} + 8 x ^{2} - 768 x ^{2} cos ^{2} ( 2 x ) - 768 x ^{2} sin ^{2} ( 2 x ) + 4 x sin ( 2 x ) + 8 k cos ^{2} ( 2 x ) + 8 k sin ^{2} ( 2 x ) + 4 cos ( 2 x ) + 384 cos ^{2} ( 2 x ) + 8 sin ^{4} ( x ) cos ( 2 x ) + 384 sin ^{2} ( 2 x ) - 16 sin ^{3} ( x ) sin ( 2 x ) cos ( x ) - sin ( 2 x ) sin ( 4 x )}{128}

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{256 x ^{4} - 16 k x ^{2} + 8 x ^{2} - 768 x ^{2} cos ^{2} ( 2 x ) - 768 x ^{2} sin ^{2} ( 2 x ) + 4 x sin ( 2 x ) + 8 k cos ^{2} ( 2 x ) + 8 k sin ^{2} ( 2 x ) + 4 cos ( 2 x ) + 384 cos ^{2} ( 2 x ) + 8 sin ^{4} ( x ) cos ( 2 x ) + 384 sin ^{2} ( 2 x ) - 16 sin ^{3} ( x ) sin ( 2 x ) cos ( x ) - sin ( 2 x ) sin ( 4 x )}{128}

(y^{^{''}} - 4 y^{^{'}} + 3 y) = 2 x + 5

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

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{e ^{- 3} x}{x}

(d^{3} + d^{2} - 4 d - 4) y = 3 e^{- x} - 4 x - 6

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

What is the solution for d^2(d^2+4)y=96x^2+sin^2(x)-k ?
The solution for d^2(d^2+4)y=96x^2+sin^2(x)-k is