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for the system:

[tex] r' = r(1-r) [/tex]

[tex] \theta' = 1 [/tex]

with

[tex]r(0) = x; \theta(0) = 0 [/tex];

the answer is

[tex]r(t) = \frac{xe^{t}}{1-x+xe^{t}} [/tex]

[tex]\theta(t) = t [/tex]

This answer was given in class as part of a process, and I can't remember how that answer is calculated. Can someone help me?