What is the solution for (d^4+4d^2)y=0 ?

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

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(d^4+4d^2)y=0

(d^{4} + 4 d^{2}) y = 0

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

Solution steps

(d^{4} + 4 d^{2}) y = 0

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 11 y = 0

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 2, y (0) = 4

2 y^{^{''}} - 7 y^{^{'}} - 4 y = 0

y^{^{''}} - 2 y^{^{'}} + 24 y = 0

35 y^{^{''''}} + 153 y^{^{''}} + 100 y = 0

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