What is the solution for (d^2y)/(dt^2)+5y=0 ?

The solution for (d^2y)/(dt^2)+5y=0 is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)

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(d^2y)/(dt^2)+5y=0

\frac{d ^{2} y}{d t ^{2}} + 5 y = 0

y = c_{1} cos (5 t) + c_{2} sin (5 t)

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 5 y = 0

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t)

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 25 y = 0, y (0) = 1, y^{^{'}} (0) = 3

y^{^{''}} + 25 y = 0, y (\frac{π}{10}) = - 3, y (π) = - 8

\frac{d ^{3} y}{d x ^{3}} - 5 y = 0

10 y^{^{''}} + 4 y^{^{'}} - 2 y = 0

What is the solution for (d^2y)/(dt^2)+5y=0 ?
The solution for (d^2y)/(dt^2)+5y=0 is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)