Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition

20

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 ...