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

The solution for d^2(d^2+4)y=96x^2 is y=c_{1}+c_{2}x+c_{3}cos(2x)+c_{4}sin(2x)+2x^4-6x^2

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d^2(d^2+4)y=96x^2

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

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + 2 x^{4} - 6 x^{2}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + 2 x^{4} - 6 x^{2}

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + 2 x^{4} - 6 x^{2}

What is the solution for d^2(d^2+4)y=96x^2 ?
The solution for d^2(d^2+4)y=96x^2 is y=c_{1}+c_{2}x+c_{3}cos(2x)+c_{4}sin(2x)+2x^4-6x^2