What is the solution for 4y^{''}+pi^2y=0 ?

The solution for 4y^{''}+pi^2y=0 is y=c_{1}cos((pit)/2)+c_{2}sin((pit)/2)

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4y^{''}+pi^2y=0

4 y^{^{''}} + π^{2} y = 0

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

Solution steps

4 y^{''} (t) + π^{2} y = 0

Solve linear ODE:

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

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

3 y^{^{'''}} + 2 y^{^{''}} = 0

2 y^{^{''}} + 28 y^{^{'}} + 99 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 14 y^{^{'}} + 45 y = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 5, y^{^{'}} (0) = 28

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 2, y^{^{'}} (0) = 13

What is the solution for 4y^{''}+pi^2y=0 ?
The solution for 4y^{''}+pi^2y=0 is y=c_{1}cos((pit)/2)+c_{2}sin((pit)/2)