(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The original problem is to solve u_t=u_xx+x with u(x,0)=0 and u(0,t)=0 by assuming there is a solution t^a*u(r), where r=x/t^b and a,b are constants

2. Relevant equations

3. The attempt at a solution

This is a long problem, so I'm not writing everything. Following the above, I have solved for a,b etc and reduced to the following problem, which is where I am stuck:

u''+r/2u'-3/2u=r

So my question is about what methods there are to solve this since it has non-constant coefficients, and I don't think I can use Laplace since I don't know u'(0). Does anyone know any other methods I could apply?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Looking for method to use in final step in heat equation problem

**Physics Forums | Science Articles, Homework Help, Discussion**