# Cauchy differential equation

Not what you're looking for? Search our solutions OR ask your own Custom question.

Prove d/dt(u(x(t),t))+tanh(x(t))(d/dx(u(x(t),t)))=0

u(x(t),0)=a(x(t))

limit as x tends to infinity of u(x,t)=0

has at most one solution.Explain why there is no boundary condition at x=0

and find a solution for the special case a(x(t))=sinh(x(t))

https://brainmass.com/math/partial-differential-equations/cauchy-partial-differential-equation-82837

#### Solution Summary

This shows why a given differential equation has at most one solution.

$2.49