The first example, which is the canonical example for this algorithm, is the following:
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| (1.1) |
The difficulty here lies on and x, and also on and y, for which an unknown a and b cannot be related together in a polynomial form.
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| (1.2) |
The same equation, even when and are replaced by arbitrary functions, can still be solved in terms of the inverses of these arbitrary functions.
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| (1.3) |
Solving gives
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| (1.4) |