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## 'A Different Differential Equation' printed from http://nrich.maths.org/

This is an investigation
concerning differential equations -- it is both difficult and
open-ended. You might wish to discuss the problem in groups and
make good use of computers or other tools to get started
before closing the problem down to explore a particular
route.

Can you find any solutions to a differential equation of the
form

$$

f'(x)= cf(x^2)\quad\mbox{ or } \quad f'(x^2)=cf(x)\,,

$$

where $c$ is a constant?