You may also like

problem icon

Which Twin Is Older?

A simplified account of special relativity and the twins paradox.

problem icon

Snookered

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

problem icon

Spokes

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

A Different Differential Equation

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?