I have a logistic issue with differential equations. I have spent four hours working on this problem and it is way past the point of ridiculous. If anyone can help out that would be great. It begins like this. dy/dt = k(P-y)*y. It is an epidemic model, where k is a positive constant relating the rate of infection. P is total population involved. An initial condition of y(0)=t is given. I am to find this particular solution. The y is multiplied. Strange that it isnt shown as ky(p-y) but perhaps its a hint that im not getting. Anyway, I am treating this as a separable equation as that is the tool we are given (the method). I have tried numerous approaches and have gotten the farthest with this one. dy/(y(p-y)= kdt Partial fractions on the left side where A and B are both = to 1/p. 1/py + 1/(p(p-y)) dy = kdt Then integrate both sides. ln(y)/p - ln(p-y)/p = kt + c. Here is where the problem begins (unless I screwed up earlier). A CAS gives me -ln(y-p) (second term left side) . Can anyone explain this? I integrated by U substitution. Why would the variable and constant be switched? I continued on assuming the CAS was correct and now I cannot isolate Y variable. I have never had this trouble before with math but hey I guess thats the way it goes. Any help would be greatly appreciated.