What is the solution for 3/4 (d^2x)/(dt^2)+72x=0,x(0)=-1/2 ?

The solution for 3/4 (d^2x)/(dt^2)+72x=0,x(0)=-1/2 is x=-1/2 cos(4sqrt(6)t)+c_{2}sin(4sqrt(6)t)

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3/4 (d^2x)/(dt^2)+72x=0,x(0)=-1/2

\frac{3}{4} \frac{d ^{2} x}{d t ^{2}} + 72 x = 0, x (0) = - \frac{1}{2}

x = - \frac{1}{2} cos (46 t) + c_{2} sin (46 t)

Solution steps

\frac{3}{4} \frac{d ^{2} x}{d t ^{2}} + 72 x = 0

Solve linear ODE:

x = - \frac{1}{2} cos (46 t) + c_{2} sin (46 t)

x = - \frac{1}{2} cos (46 t) + c_{2} sin (46 t)

y^{^{''}} - 16 y^{^{'}} + 73 y = 0

y^{^{''}} - 8 y^{^{'}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 3

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

4 y^{^{''}} - 5 y^{^{'}} + y = 0

y^{^{''}} - (1 + 2) y^{^{'}} + 21 y = 0

What is the solution for 3/4 (d^2x)/(dt^2)+72x=0,x(0)=-1/2 ?
The solution for 3/4 (d^2x)/(dt^2)+72x=0,x(0)=-1/2 is x=-1/2 cos(4sqrt(6)t)+c_{2}sin(4sqrt(6)t)