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First order linear equation
In the equation of the form:
y` + P(x)y = Q(x)
Can the y in P(x)y be equal to something like e^y or siny and not really y. And then we find the integrating factor using e^(integral (P(x))).
y` + P(x)y = Q(x)
Can the y in P(x)y be equal to something like e^y or siny and not really y. And then we find the integrating factor using e^(integral (P(x))).
If you can get your hands on one, look at a proof that the integrating factor method works for the equation y' + P(x)y = Q(x). It's a really nice and not too difficult proof IIRC. If in doubt, I can't imagine google failing to throw one up.
You'll soon see that the proof relies on the fact that you specifically need P(x)y, rather than say P(x)e^y (or similar). Therefore, the answer is no.
You'll soon see that the proof relies on the fact that you specifically need P(x)y, rather than say P(x)e^y (or similar). Therefore, the answer is no.
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