What is the solution for (d^2x)/(dt^2)+81x=0 ?

The solution for (d^2x)/(dt^2)+81x=0 is x=c_{1}cos(9t)+c_{2}sin(9t)

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(d^2x)/(dt^2)+81x=0

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

x = c_{1} cos (9 t) + c_{2} sin (9 t)

Solution steps

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

Solve linear ODE:

x = c_{1} cos (9 t) + c_{2} sin (9 t)

x = c_{1} cos (9 t) + c_{2} sin (9 t)

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

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

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

15 y^{^{''''}} + 128 y^{^{''}} + 25 y = 0

y^{^{''}} + 8 y^{^{'}} + 7 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for (d^2x)/(dt^2)+81x=0 ?
The solution for (d^2x)/(dt^2)+81x=0 is x=c_{1}cos(9t)+c_{2}sin(9t)