What is the solution for (d^2x)/(dt^2)=-49x ?

The solution for (d^2x)/(dt^2)=-49x is x=c_{1}cos(7t)+c_{2}sin(7t)

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(d^2x)/(dt^2)=-49x

\frac{d ^{2} x}{d t ^{2}} = - 49 x

x = c_{1} cos (7 t) + c_{2} sin (7 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} = - 49 x

Solve linear ODE:

x = c_{1} cos (7 t) + c_{2} sin (7 t)

x = c_{1} cos (7 t) + c_{2} sin (7 t)

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 1, y (1) = 3

y^{^{''''}} - 5 y^{^{'''}} + 5 y^{^{''}} + 5 y^{^{'}} - 6 y = 0

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

y^{^{''}} = - y^{^{'}}

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

What is the solution for (d^2x)/(dt^2)=-49x ?
The solution for (d^2x)/(dt^2)=-49x is x=c_{1}cos(7t)+c_{2}sin(7t)