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

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

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(d^2x)/(dt^2)=-k*x

\frac{d ^{2} x}{d t ^{2}} = - k \cdot x

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} = - k \cdot x

Solve linear ODE:

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

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

\int 9 sec^{2} (x) d x

x + ln (x)

\frac{x ^{5}}{2 - x ^{4}}

y = (x^{4} + 1)^{5}

\frac{d x}{d t} = 6 (x^{2} + 1), x (\frac{π}{4}) = 1

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