What is the solution for (d^2x)/(dt^2)+64x=0 ?

The solution for (d^2x)/(dt^2)+64x=0 is x=c_{1}cos(8t)+c_{2}sin(8t)

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(d^2x)/(dt^2)+64x=0

\frac{d ^{2} x}{d t ^{2}} + 64 x = 0

x = c_{1} cos (8 t) + c_{2} sin (8 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 64 x = 0

Solve linear ODE:

x = c_{1} cos (8 t) + c_{2} sin (8 t)

x = c_{1} cos (8 t) + c_{2} sin (8 t)

4 y^{^{''}} = - y^{^{'}}

x^{^{''}} + 2 x^{^{'}} + 5 x = 0

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + y = 0, y^{^{'}} (0) = 6, y (1) = 8

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

What is the solution for (d^2x)/(dt^2)+64x=0 ?
The solution for (d^2x)/(dt^2)+64x=0 is x=c_{1}cos(8t)+c_{2}sin(8t)