What is the solution for (d^5+8d^3+16d)y=0 ?

The solution for (d^5+8d^3+16d)y=0 is y=c_{1}+c_{2}cos(2x)+c_{3}sin(2x)+x(c_{4}cos(2x)+c_{5}sin(2x))

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(d^5+8d^3+16d)y=0

(d^{5} + 8 d^{3} + 16 d) y = 0

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + x (c_{4} cos (2 x) + c_{5} sin (2 x))

Solution steps

(d^{5} + 8 d^{3} + 16 d) y = 0

Solve linear ODE:

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + x (c_{4} cos (2 x) + c_{5} sin (2 x))

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + x (c_{4} cos (2 x) + c_{5} sin (2 x))

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y (1) = 0

\frac{d ^{2} x}{d t ^{2}} + 81 x = 0

\frac{1}{4} y^{^{''}} + y^{^{'}} + 4 y = 0

y^{^{'''}} + 5 y^{^{''}} + 3 y^{^{'}} - 9 y = 0

y^{^{'''}} + 2 y^{^{'}} - 3 y = 0

What is the solution for (d^5+8d^3+16d)y=0 ?
The solution for (d^5+8d^3+16d)y=0 is y=c_{1}+c_{2}cos(2x)+c_{3}sin(2x)+x(c_{4}cos(2x)+c_{5}sin(2x))