What is the solution for 4(d^2x)/(dt^2)+324x=0 ?

The solution for 4(d^2x)/(dt^2)+324x=0 is x=c_{1}cos(9t)+c_{2}sin(9t)

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4(d^2x)/(dt^2)+324x=0

4 \frac{d ^{2} x}{d t ^{2}} + 324 x = 0

x = c_{1} cos (9 t) + c_{2} sin (9 t)

Solution steps

4 \frac{d ^{2} x}{d t ^{2}} + 324 x = 0

Solve linear ODE:

x = c_{1} cos (9 t) + c_{2} sin (9 t)

x = c_{1} cos (9 t) + c_{2} sin (9 t)

y^{^{'''}} - 20 y^{^{''}} + 111 y^{^{'}} - 180 y = 0

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 2, y^{^{'}} (0) = 0

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (1) = 5

2 y^{^{''}} - 2 y^{^{'}} + y = 0, y^{0} = - 1, y^{^{'}} 0 = 0

y^{^{''}} + 2 y^{^{'}} - 6 y = 0

What is the solution for 4(d^2x)/(dt^2)+324x=0 ?
The solution for 4(d^2x)/(dt^2)+324x=0 is x=c_{1}cos(9t)+c_{2}sin(9t)