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

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

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(d^2y)/(dt^2)+16y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 8 x = 0

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 8 x = 0

x \cdot y^{^{''}} + 2 x \cdot y^{^{'}} + x \cdot y = 0

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} - 4 y = 0

y^{^{''''}} + 2 y^{^{'''}} + y^{^{''}} = 0

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