Posted by Subhotosh Khan on August 09, 2002 at 08:24:17:
In Reply to: Re: If you read the text book carefully.... posted by Colin on August 09, 2002 at 02:12:31:
: : : The question starts by asking us to "prove that the equation: dy/dx = (y-4x)/(x-y) is not separable..."
: : : How does one provide such a proof, which is definitive (conclusive)? I'm not sure how to phrase and approach such a proof. Any tips? Thank you,
: : : Colin
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: : You will find there is a necessary condition for "separable-variable" first order differential equations.
: : Read it and thou shall learn....
: So is it that you must be able to isolate variables of each type on opposite sides of the equals sign?
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Suppose your ODE is in the form below:
f_1(x,y) dx = f_2 (x,y) dy
Now there is a relationship between"partial differential" of f_1 and f_2 that must be satisfied.