- #1

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The final step of solving a separable ODE is to find a function, f, defined implicitly by a relation

G(y) = H(x).

Say G(y) isn't defined at y = a and H(x) isn't defined at x = b, it appears to me that when rearranging such a relation to put y in terms of x, the point at which G(y) isn't defined isn't 'important' because it doesn't correspond to a point where y = f(x) is defined anyway.

Is this the case and if so, why?

__Example__

H(y) = G(x) = 1 / (y-1) = x

H(y) defined for all real values except y = 0

G(x) defined for all real values.

Rearrangement gives,

y = f(x) = 1 + 1 / x

and no value of x will solve f(x) = 1

Cheers