If You consider that the ODE becomes separable...
Kind regards
I've got an ODE that I'm not even sure how to start with:
As far as I can tell, it's not homogeneous, not seperable, not linear, and not exact.
I'm not sure what approach to take. Can someone help me figure out where to start?
Okay, if I do that, I can factor out the , leaving the y terms grouped.
Is this supposed to be seperable? The seperable equations I've worked with were all multiplation/division at the top most levels though, whereas in this case, we have subtraction going on.
What you reminded me of definitely helped, but I'm still uncertain how to work with this.
All right!... so we can separate the variables obtaining...
(1)
The next step now is to integrate both terms of (1). The integral in the x is not a problem... regarding the integral...
(2)
... we can see an important detail: is the negate of derivative of ... what does it suggest that?...
Kind regards
Ah, but this is the beauty of DE's: it's quite straight-forward, usually, to check your own answer. Just plug it into the original DE and see if you get equality. What do you get?
Incidentally, there are two things you should always do when solving a DE. One is to check your answer by plugging back into the DE. The other is to determine the intervals of validity of the solution.
Quite right. I didn't say you made a mistake. If you did, it might have something to do with a possibly unjustified elimination of absolute value signs. I think that, if anything, there might be some sign errors in your answer. Mathematica gives the answer as
which is equivalent to
Comparing this with your answer, you can see that there are sign differences in the exponential.
Why? You've already integrated, so there shouldn't be any differentials in sight.That being said, would inverting the fraction not result in a 1/dx and 1/dy condition as well?
Is that an indication that I made a mistake or is that just another way of writing the same answer?
Because when I plug either what I got or what you posted into WolframAlpha as part of the original ODE, I don't get a result of zero with either one.
You quoted a section with six lines and didn't specify which one you were referring to. I thought you meant the first, as it was the most obvious fraction, and the last line of the section you quoted was a case where I *had* inverted the fractions. I had no choice but to guess what you were referencing.