Age 16 to 18 Challenge Level:
The key for this problem is for students to appreciate that the
signs in differential equations are of crucial importance in
determining the structure of a solution. They can make the
difference between solutions growing to infinity, oscillating or
settling down to zero.
When constructing differential equations using, for example, $F \;
= \; ma$, negative signs on the right hand side correspond to
'repulsions' and positive signs correspond to 'attractions'.
Understanding the structure of equations in this way is a very
powerful approach which can transcend the details of the algebraic