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

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

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-y^{''}-9*pi^2y=0

- y^{^{''}} - 9 \cdot π^{2} y = 0

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

Solution steps

- y^{''} (t) - 9 \cdot 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)

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 324 x = 0

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = 23

2 y^{^{''}} - 13 y^{^{'}} + 20 y = 0, y (0) = - 2, y^{^{'}} (0) = - 11

4 y^{^{''}} + 20 y^{^{'}} + 29 y = 0, y (1) = 8

y^{^{''}} - 3 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 5

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