Partial differential equations: general and particular solutions
20.1 Determine whether the following can be written as functions of p = x2 + 2y only, and hence whether they are solutions of
(a) x2(x2 − 4) + 4y(x2 − 2) + 4(y2 − 1);
(b) x4 + 2x2y + y2;
(c) [x4 + 4x2y + 4y2 + 4]/[2x4 + x2(8y + 1) + 8y2 + 2y].
As a first step, we verify that ...