A different differential equation
Explore the properties of this different sort of differential
equation.
Age
16 to 18
Challenge level
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?