# Second order equation help

hello every body .I have some problem :
i don't know slove the equation
$$x"=k/m*x$$ (1)
i don't understand result of (1) is $$x=Asinkt+Bcoskt$$

Related Introductory Physics Homework Help News on Phys.org
CompuChip
Homework Helper
There are two independent solutions, because it is a second order equation. They are sine and cosine. The general solution is then a linear combination of both, as you can check by just plugging it into the differential equation.

i know this thing. But i don't know the way to slove this equation
who can help me. thank you very much

CompuChip
If you know about complex numbers, there is a more elegant way (which also works for more general equations). That is to plug in a trial solution $x = e^{\lambda t}$. Then the differential equation will give you an equation for $\lambda$, whose roots provide the n independent solutions (for an n-th order differential equation, in this case, n = 2).
$$e^{i\theta} = \cos\theta + i \sin\theta$$