What is the solution for (d^2x)/(dt^2)+x=0 ?

The solution for (d^2x)/(dt^2)+x=0 is x=c_{1}cos(t)+c_{2}sin(t)

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(d^2x)/(dt^2)+x=0

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

x = c_{1} cos (t) + c_{2} sin (t)

Solution steps

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

Solve linear ODE:

x = c_{1} cos (t) + c_{2} sin (t)

x = c_{1} cos (t) + c_{2} sin (t)

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

y^{^{''}} - 14 y^{^{'}} + 49 y = 0, y (0) = 0, y^{^{'}} = 7

y^{^{''}} - 9 y^{^{'}} + 9 y = 0

y^{^{'''}} + 2 y^{^{''}} - 16 y^{^{'}} - 32 y = 0

x^{^{''}} - a^{2} x = 0

What is the solution for (d^2x)/(dt^2)+x=0 ?
The solution for (d^2x)/(dt^2)+x=0 is x=c_{1}cos(t)+c_{2}sin(t)