What is the solution for y^{''}+a/4 y=0 ?

The solution for y^{''}+a/4 y=0 is y=c_{1}cos((sqrt(a)t)/2)+c_{2}sin((sqrt(a)t)/2)

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y^{''}+a/4 y=0

y^{^{''}} + \frac{a}{4} y = 0

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

Solution steps

y^{''} (t) + \frac{a}{4} y = 0

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = 1

y^{^{''}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = 2

y^{^{'''}} + 8 y^{^{''}} + 21 y^{^{'}} + 18 y = 0

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

22 y^{^{''''}} + 61 y^{^{''}} + 25 y = 0

What is the solution for y^{''}+a/4 y=0 ?
The solution for y^{''}+a/4 y=0 is y=c_{1}cos((sqrt(a)t)/2)+c_{2}sin((sqrt(a)t)/2)