1. The problem statement, all variables and given/known data Consider the nonlinear (ordinary) differential equation u' = u(1-u). a) Show that u_1 (x) = e^x/(1+e^x) and u_2(x) = 1 are solutions. b) Show that u_1+u_2 is not a solution. c) For which values of c is cu_1 a solution? How about cu_2 ? 2. Relevant equations N/a 3. The attempt at a solution a) To show that they are a solution I plugged in the corresponding u_1 and u_2 into the equations and proved equality. b) To show that this is not a solution, I did the same. c) This is where I am having trouble, here is my strategy: We observe c*u_2 first. we know u_2' = 0 so from u'=u(1-u) we have c*u' = 0 and we know that 1*c = c so on the right hand side we have c(1-c) and so we have: c-c^2 =0 This means c is either 0 or 1. This doesn't seem right, there seems to be a better way (perhaps involving differential equations knowledge) to solve for c. I would imagine c could be in the form e^x of some sort. Similarly with c*u_1 I am finding equally difficult problems where c = 0.