What is the solution for (d^2x)/(dt^2)+16*x=0 ?

The solution for (d^2x)/(dt^2)+16*x=0 is x=c_{1}cos(4t)+c_{2}sin(4t)

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(d^2x)/(dt^2)+16*x=0

\frac{d ^{2} x}{d t ^{2}} + 16 \cdot x = 0

x = c_{1} cos (4 t) + c_{2} sin (4 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 16 \cdot x = 0

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t)

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = 5

x^{^{''}} + 4 x^{^{'}} + 29 x = 0

y^{^{'''}} + 2 y^{^{''}} - 6 y^{^{'}} - 72 y = 0, y (0) = e^{4 x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 2

y^{^{''''}} + 4 y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + \frac{1}{2} y = 0

What is the solution for (d^2x)/(dt^2)+16*x=0 ?
The solution for (d^2x)/(dt^2)+16*x=0 is x=c_{1}cos(4t)+c_{2}sin(4t)