Solve the boundary problem u''= 0 for 0 < x < 1 with u'(0) + ku(0) = 0 and u'(1) +/- ku(1) = 0. Do the + and - cases separately. What is special about the case k = 2?
Any help would be greatly appreciated!
"PDE" usually stands for "partial differential equations" but I see only one independent variable here. In any case, this looks like direct integration will do it. If u"= 0, then u'= C, a constant, and so u(x)= Cx+ D where D is another constant. Can you continue from there? (Actually both k= 0 and k= 2 are special.)