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

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

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

- y^{^{''}} - π^{2} y = 0

y = c_{1} cos (π t) + c_{2} sin (π t)

Solution steps

- y^{''} (t) - π^{2} y = 0

Solve linear ODE:

y = c_{1} cos (π t) + c_{2} sin (π t)

y = c_{1} cos (π t) + c_{2} sin (π t)

y^{^{''}} + 20 y^{^{'}} + 100 y = 0, y (0) = 2, y^{^{'}} (0) = 1

\frac{d ^{2} v}{d x ^{2}} + k^{2} v = 0

4 \frac{d y}{d x} - \frac{d ^{2} y}{d x ^{2}} = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3, y (- 1) = 5

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

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