When you face a difficult problem try to solve another more simple and related. So instead of
finding the solutions of the differential equations we must seek for how many there are. But an
unexpected result is the format of the answer: we get not a number but a solution expressed in
terms of a geometrical shape. That is quite unusual for our students.
A simple analogue can be looked at triangles and quadrangles in the plane. It can be
complicated to find the angles in the corners of some of these figures, but sometimes, before
Euclid, someone realised that the sum of the angles in all the corners is always 180 degrees for
a triangle, and 360 degrees for a quadrangle. The answer to this question is thus easily given,
and depends only on the shape of the figure, namely whether it has three or four vertices.
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