1st order Differential equation help

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#1
Hi,How do I get the differential equation below into the form dy/dx P(x)y=Q(x) so that I can use e^INTEGRALofP(x) as the integrating factor? As there is no y on its own to figre out P(x).Thank you
Last edited by Rhys_M; 4 weeks ago
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4 weeks ago
#2
I'm not sure if it's possible to do so in this question( i haven't actually tried but nothing leaps out immediately, someone else may be able to find a way?)
Have you tried solving it by separating the variables? It seems like the more natural thing to do
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4 weeks ago
#3
Agree. Separate variables.
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4 weeks ago
#4
(Original post by Rhys_M)
Hi,How do I get the differential equation below into the form dy/dx P(x)y=Q(x) so that I can use e^INTEGRALofP(x) as the integrating factor? As there is no y on its own to figre out P(x).Thank you
Side note: it always helps if you upload a picture of the original question with any context, so that people can see if you've been given any additional info like what approach to take to solve the DE, or what method to use, or (if it's from a book) which chapter or section it comes from because it may be testing you on a particular method

Just at a glance it looks like writing u = e^y may help because then du/dx = (du/dy)(dy/dx) = e^y(dy/dx) and you get a simpler DE involving du/dx, u and x, but I may be misleading you here if that's not the intended approach
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4 weeks ago
#5
I just tried it and if you use separation of variables after your 2nd line, it works out really nicely

It's best to post the original question though if you are able to
Last edited by Driving_Mad; 4 weeks ago
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4 weeks ago
#6
by inspection the LHS is the exact derivative of x2ey
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4 weeks ago
#7
(Original post by the bear)
by inspection the LHS is the exact derivative of x2ey
<Hobbit>: I don't think they know about exact derivatives, Bear.
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