- #1
KenBakerMN
- 11
- 2
It's been a little too long since I've has to do this. Can someone please remind me, how do you get from:
∂u/∂t = C(∂u/∂g)
to
∂^2u/∂t^2 = (C^2)(∂^2u/∂t^2)
The notation here is a little clumsy, but I'm just taking the second PDE of each side. How does the C^2 get there? Seems like it ought to be C but I can't put my finger on a proof either way.
By the way, this comes up in a derivation of the wave equation:
∂^2u/∂x^2 = (1/c^2)(∂^2u/∂t^2)
starting from
u(x,t) = u(x ± ct)
I'm sure someone out there knows this. Thanks for your help.
∂u/∂t = C(∂u/∂g)
to
∂^2u/∂t^2 = (C^2)(∂^2u/∂t^2)
The notation here is a little clumsy, but I'm just taking the second PDE of each side. How does the C^2 get there? Seems like it ought to be C but I can't put my finger on a proof either way.
By the way, this comes up in a derivation of the wave equation:
∂^2u/∂x^2 = (1/c^2)(∂^2u/∂t^2)
starting from
u(x,t) = u(x ± ct)
I'm sure someone out there knows this. Thanks for your help.