What is the solution for x^{''}+1536/25 x=0 ?

The solution for x^{''}+1536/25 x=0 is x=c_{1}cos((16sqrt(6)t)/5)+c_{2}sin((16sqrt(6)t)/5)

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x^{''}+1536/25 x=0

x^{^{''}} + \frac{1536}{25} x = 0

x = c_{1} cos (\frac{16 6 t}{5}) + c_{2} sin (\frac{16 6 t}{5})

Solution steps

x^{''} (t) + \frac{1536}{25} x = 0

Solve linear ODE:

x = c_{1} cos (\frac{16 6 t}{5}) + c_{2} sin (\frac{16 6 t}{5})

x = c_{1} cos (\frac{16 6 t}{5}) + c_{2} sin (\frac{16 6 t}{5})

10 y^{^{''}} + 40 y^{^{'}} + 240 y = 0

x^{^{''}} + 2 x^{^{'}} + 3 x = 0, x (0) = 1, x^{^{'}} (0) = 0

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

y^{^{''}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 4

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

What is the solution for x^{''}+1536/25 x=0 ?
The solution for x^{''}+1536/25 x=0 is x=c_{1}cos((16sqrt(6)t)/5)+c_{2}sin((16sqrt(6)t)/5)