Online Library → Charles Babbage → Examples of the solutions of functional equations → online text (page 2 of 2)

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equations

(33)

dyj^jx, y) _ _ (j y^ja â€¢- Xf h - y)

dy dx

_ d\l^(a â€” x, bâ€”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 = -â€”

o -\- C X

(65). Given ^ (2a - j:) = x/.Â» x.

Put y^yX = (pâ€”'fipX,

then \lr'^X=:(}> â€” ^f(p

(33)

dyj^jx, y) _ _ (j y^ja â€¢- Xf h - y)

dy dx

_ d\l^(a â€” x, bâ€”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 = -â€”

o -\- C X

(65). Given ^ (2a - j:) = x/.Â» x.

Put y^yX = (pâ€”'fipX,

then \lr'^X=:(}> â€” ^f(p

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Online Library → Charles Babbage → Examples of the solutions of functional equations → online text (page 2 of 2)