Following the hint, I attempted making the above equation homogenous, but I couldn't figure out how to.
Solve the first order differential equation
1
$\begingroup$
ordinary-differential-equations
1 Answers
6
We have $(\ln y)'= \frac{y'}{y}$. Hence, if you use the hint and if you put $z= \ln y$, then you get the equation
$z'=-1-\frac{1}{x}z$
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1All too easy. Well done Fred. (+1) ... I would say that the "hint" is a bit misleading. It should read, "Divide both sides of the equation by $y$." – 2017-02-22
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0@Fred Why is the answer z' = ...? Doesn't solving the differential equation mean that the answer should be y = ...? Also, how did you come up with (lny)' = y'/y? I don't think I would be able to guess that on a test – 2017-02-22
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0So how to solve this diff eq for z? (assuming prime means derivative w.r.t. x) – 2017-02-22
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0@lalala This can be solved using an [Integrating Factor](http://mathworld.wolfram.com/IntegratingFactor.html) or with [Variation of Parameters](https://en.m.wikipedia.org/wiki/Variation_of_parameters). – 2017-02-22