Hi,
Let v(x,t) = u(x+ct,t).
Find partial of v with respect to x, second partial of v with respect to x and the partial with respect to t.
I'm just confused with the t's acting as x+ct and t by it self.
Thanks
It's all about the chain rule. Think of your function u this way:
$\displaystyle v(x, t) = u(z, t)$ where $\displaystyle z = x + ct$.
So
$\displaystyle v_x = u_z \cdot \frac{\partial z}{\partial x} = u_z$
Then replace z with x + ct.
$\displaystyle v_t = u_z \cdot \frac{\partial z}{\partial t} + u_t$
-Dan