What is the solution for y^{''}+9pi^2y=0 ?

The solution for y^{''}+9pi^2y=0 is y=c_{1}cos(3pit)+c_{2}sin(3pit)

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y^{''}+9pi^2y=0

y^{^{''}} + 9 π^{2} y = 0

y = c_{1} cos (3 π t) + c_{2} sin (3 π t)

Solution steps

y^{''} (t) + 9 π^{2} y = 0

Solve linear ODE:

y = c_{1} cos (3 π t) + c_{2} sin (3 π t)

y = c_{1} cos (3 π t) + c_{2} sin (3 π t)

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 5

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y^{^{'}} (0) = 2, y (0) = 1

36 y^{^{''}} + 25 y = 0

2 y^{^{''}} - 17 y^{^{'}} - 9 y = 0, y (0) = 4, y^{^{'}} (0) = - 7

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

What is the solution for y^{''}+9pi^2y=0 ?
The solution for y^{''}+9pi^2y=0 is y=c_{1}cos(3pit)+c_{2}sin(3pit)