What is the solution for (d^2x)/(dt^2)=-pi^2x ?

The solution for (d^2x)/(dt^2)=-pi^2x is x=c_{1}cos(pit)+c_{2}sin(pit)

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(d^2x)/(dt^2)=-pi^2x

\frac{d ^{2} x}{d t ^{2}} = - π^{2} x

x = c_{1} cos (π t) + c_{2} sin (π t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} = - π^{2} x

Solve linear ODE:

x = c_{1} cos (π t) + c_{2} sin (π t)

x = c_{1} cos (π t) + c_{2} sin (π t)

u^{^{''}} + 0.25 u^{^{'}} + H (t) = 0

y^{^{'''}} - 23 y^{^{''}} + 160 y^{^{'}} - 300 y = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (π) = 7, y (0) = 7

y^{^{''}} - 4 y^{^{'}} + 5 y = 0

y^{^{''}} + 5 y^{^{'}} + 5 y = 0

What is the solution for (d^2x)/(dt^2)=-pi^2x ?
The solution for (d^2x)/(dt^2)=-pi^2x is x=c_{1}cos(pit)+c_{2}sin(pit)