- #1
Ted Burgess
- 5
- 0
Hi,
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
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