What is the solution for (d^4+8d^2+16)*y=-2 ?

The solution for (d^4+8d^2+16)*y=-2 is y=c_{1}cos(2x)+c_{2}sin(2x)+x(c_{3}cos(2x)+c_{4}sin(2x))-1/8

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(d^4+8d^2+16)*y=-2

(d^{4} + 8 d^{2} + 16) \cdot y = - 2

y = c_{1} cos (2 x) + c_{2} sin (2 x) + x (c_{3} cos (2 x) + c_{4} sin (2 x)) - \frac{1}{8}

Solution steps

(d^{4} + 8 d^{2} + 16) y = - 2

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + x (c_{3} cos (2 x) + c_{4} sin (2 x)) - \frac{1}{8}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + x (c_{3} cos (2 x) + c_{4} sin (2 x)) - \frac{1}{8}

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

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

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

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

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

What is the solution for (d^4+8d^2+16)*y=-2 ?
The solution for (d^4+8d^2+16)*y=-2 is y=c_{1}cos(2x)+c_{2}sin(2x)+x(c_{3}cos(2x)+c_{4}sin(2x))-1/8