What is the solution for 1/8 x^{''}+16x=0 ?

The solution for 1/8 x^{''}+16x=0 is x=c_{1}cos(8sqrt(2)t)+c_{2}sin(8sqrt(2)t)

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1/8 x^{''}+16x=0

\frac{1}{8} x^{^{''}} + 16 x = 0

x = c_{1} cos (82 t) + c_{2} sin (82 t)

Solution steps

\frac{1}{8} x^{''} (t) + 16 x = 0

Solve linear ODE:

x = c_{1} cos (82 t) + c_{2} sin (82 t)

x = c_{1} cos (82 t) + c_{2} sin (82 t)

y^{^{'''}} - 27 y^{^{''}} + 243 y^{^{'}} - 729 y = 0

y^{^{''}} + 4 y = 0, y^{^{'}} (3 π) = 4, y (0) = 4

y^{^{''}} + 3 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 8

10 y^{^{''}} + 11 y^{^{'}} + 3 y = 0

y^{^{'''}} - 5 y^{^{''}} + 3 y + 9 y = 0

What is the solution for 1/8 x^{''}+16x=0 ?
The solution for 1/8 x^{''}+16x=0 is x=c_{1}cos(8sqrt(2)t)+c_{2}sin(8sqrt(2)t)