Thread: Partial Differential Question

Hi! Haven't been on here for ages.

I'm a little confused about part of a question I'm doing. I won't write it all out, but basically u=u(x(s,r), t(s,r))







From that we supposedly get t = s + A(r) which I do understand, but also:
x=B(r)exp(3s) and u=A(r)exp(-s).

Maybe I'm a bit too tired to be doing this, but where do the exponentials come from?

Thanks!

They are just solving the other equations



The is a constant of integration, but it is only constant with respect to not because we used partial integration to undo the partial derivative.

The u equation is solved exactly the same way! your initial conditions will define the arbitrary constants(functions)