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!