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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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