What is the solution for y^{''}+((0.5)/2)y=0 ?

The solution for y^{''}+((0.5)/2)y=0 is y=c_{1}cos(t/2)+c_{2}sin(t/2)

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y^{''}+((0.5)/2)y=0

y^{^{''}} + (\frac{0.5}{2}) y = 0

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2})

Solution steps

y^{''} (t) + (\frac{0.5}{2}) y = 0

Solve linear ODE:

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2})

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2})

45 x^{^{''}} + 120 x^{^{'}} + 15 x = 0

64 y - 16 y^{^{'}} - 4 y^{^{''}} + y^{^{'''}} = 0

y^{^{''}} - 5 y^{^{'}} + 12 y = 0, y (2) = 0, y^{^{'}} (2) = - 4

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

v^{^{''}} + v^{^{'}} \cdot 1000 + v \cdot 125000 = 0

What is the solution for y^{''}+((0.5)/2)y=0 ?
The solution for y^{''}+((0.5)/2)y=0 is y=c_{1}cos(t/2)+c_{2}sin(t/2)