What is the solution for (d^2)/(dt^2)(θ(t))+gθ(t)=0 ?

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

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(d^2)/(dt^2)(θ(t))+gθ(t)=0

\frac{d ^{2}}{d t ^{2}} (θ (t)) + g θ (t) = 0

θ (t) = c_{1} cos (g t) + c_{2} sin (g t)

Solution steps

\frac{d ^{2}}{d t ^{2}} (θ (t)) + g θ (t) = 0

Solve linear ODE:

θ (t) = c_{1} cos (g t) + c_{2} sin (g t)

θ (t) = c_{1} cos (g t) + c_{2} sin (g t)

15 y^{^{''}} + 90 y^{^{'}} + 135 y = 0, y (0) = 3, y^{^{'}} (0) = 0

12 y^{^{''}} + 64 y = 0, y (0) = 4, y^{^{'}} (0) = 7

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 0.9

y^{^{''}} - 8 y^{^{'}} + 25 y = 0, y (0) = e^{4 x} cos (3 x)

81 y^{^{''''}} = 256 y

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