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anonymous
 4 years ago
Can someone help me solve this differential equation?
dy/dx = y/x + e^(y/x)
anonymous
 4 years ago
Can someone help me solve this differential equation? dy/dx = y/x + e^(y/x)

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so far what I've done is subsitute v = y/x I'm just haveing some trouble with what to do with the dy/dx after the subsitution

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it is a fairly drawn out process... have you checked out http://tutorial.math.lamar.edu/Classes/DE/Substitutions.aspx

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that website has the answer do your exact question, just follow the steps

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0After you put y=vx. you get dy/dx= v+ xdv/dx. dy/dx=v+e^v. v cancels you get e^v=xdv/dx. e^v dv=dx/x. e^v+log x=c.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so as far as I can tell you islate y y=vx then take the derivative in terms of x on both sides to get dy/dx = (dv/dx)x + v

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmm so I have (1/e^v) dv = (1/x) dx now

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then do I just try and solve this new thing like a seperable differential equation?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0integrate both sides integral of e^x dx is e^x and integral of 1/x is ln x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so now I have e^v = lnx + C

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0now I can just subsitute y/x back in and take the ln to isolate the y?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0v=y/x so substitue back to get the equation in terms of y and x.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so I have (y/x)*lne = ln(lnx + C) then y = x*ln(lnx + C)  lne

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ln e=1. yeah it is correct.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so just y = x*ln(lnx + C)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Hold on Theres a negative sign too. it is e^(y/x). So taking ln leaves a minus sign too.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oops then y = x*ln(lnx + C)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah this shld be rite.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0alright thanks a lot!
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