5. There is a distribution ψ such that ∫ψ(x)u(x)dx (intergral is from -infinity to +infinity) = ∫xu′(x)dx (integral is from 0 to 1)

Write ψ(x) as a sum of Delta derivatives, ordinary functions, and Dirac Delta functions.

6. The equation uxx + 2uux = δ′(x). If you were solving this equation piecewise, what jump conditions would you need to use at x = 0 to make u a weak solution?