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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} + 6 y^{^{''}} - 37 y^{^{'}} - 90 y = 0

9 y^{^{''}} + y = 0, y (0) = - 2, y^{^{'}} (0) = 1

u, \frac{d ^{2} u}{d x ^{2}} = a u (x)

y^{^{''}} - 7 y^{^{'}} + 8 y = 0, y (0) = 2, y^{^{'}} (0) = 7

y^{^{''}} + 3 y^{^{'}} - 18 y = 0, y (0) = 3, y^{^{'}} (0) = 18

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