What is the solution for (d^2x)/(dt^2)+9x=0 ?

The solution for (d^2x)/(dt^2)+9x=0 is x=c_{1}cos(3t)+c_{2}sin(3t)

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(d^2x)/(dt^2)+9x=0

\frac{d ^{2} x}{d t ^{2}} + 9 x = 0

x = c_{1} cos (3 t) + c_{2} sin (3 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 9 x = 0

Solve linear ODE:

x = c_{1} cos (3 t) + c_{2} sin (3 t)

x = c_{1} cos (3 t) + c_{2} sin (3 t)

y^{^{''}} - 169 y = 0

y^{^{'''}} - 17 y^{^{''}} + 82 y^{^{'}} - 120 y = 0

16 y^{^{''}} - 56 y^{^{'}} + 49 y = 0

y^{^{''}} = 4 y, y (0) = 1, y (1) = 0

y^{^{''}} - 4 a^{2} y^{^{'}} + y = 0

What is the solution for (d^2x)/(dt^2)+9x=0 ?
The solution for (d^2x)/(dt^2)+9x=0 is x=c_{1}cos(3t)+c_{2}sin(3t)