text: Integrating u'=u, gives u(t)=u(0)e^t. Finding u(0) near 0 so that u(T)=2 gives u(0)=u(T) e^-T. But if you integrate backwards u(T-t)=u(T)e^-t and you can approximate u(0)=u(T)e^{-T} to a reasonable accuracy. e.g. Backward Euler instead of Forward Euler. Too subtle?