What is the solution for (d^2y)/(dt^2)+25y=0 ?

The solution for (d^2y)/(dt^2)+25y=0 is y=c_{1}cos(5t)+c_{2}sin(5t)

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(d^2y)/(dt^2)+25y=0

\frac{d ^{2} y}{d t ^{2}} + 25 y = 0

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

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 25 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^{^{'''}} + 9 y^{^{''}} = 0

y^{^{''}} + 36 y = 0, y (π) = 0, y (0) = 0

y^{^{'''}} - 8 y^{^{''}} = 0

y^{^{'''}} - y^{^{''}} - 56 y^{^{'}} = 0

y^{^{''}} + y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 1

What is the solution for (d^2y)/(dt^2)+25y=0 ?
The solution for (d^2y)/(dt^2)+25y=0 is y=c_{1}cos(5t)+c_{2}sin(5t)