Examples of the solutions of functional equations online

equations



(33)

dyj^jx, y) _ _ (j y^ja •- Xf h - y)
dy dx

_ d\l^(a — x, b—y) _ dy\^{x, y)
dy dx

If the first of these be difFerentiated relative to y, and the
second relative to x ; then the right side of the first resulting
equation vi^Ill be identical with the left side of the second,
and we shall have

d" x^ (^r, y) ^ d'xl. (x, y) ,
dy^ dx"

the solution of this partial differential equation is

^ (J-, y)=(p{x + y) ^\rX = -—

o -\- C X



(65). Given ^ (2a - j:) = x/.» x.

Put y^yX = (p—'fipX,

then \lr'^X=:(}> — ^f(p