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Cannot solve - dy/dx = (e^(1/x))/(x*((x+1)^2))

  • Thread starter manjanjatx
  • Start date
  • #1

Homework Statement



Solve the following differential equation:

y' = (e^(1/x)) / (x*((x+1)^2))

Homework Equations



?

The Attempt at a Solution



I wasted over 5 hours trying to solve this equation, but was unable to get a proper solution. Wolfram Alpha and Maple gave me the correct answer (the solution works in the differential equation), but were unable to elaborate. Any help would be appreciated!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Gib Z
Homework Helper
3,346
5
Welcome to PF.

So you just need to integrate your right hand side. From the looks of it, you should first let [itex] u = \frac{1}{x} [/itex] .
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
12,985
540
1. Your ODE is

[tex] \frac{dy}{dx} = \frac{e^{\frac{1}{x}}}{x(x+1)^2} [/tex]

Change the variable [itex] x=\frac{1}{p} [/itex]

Separate the new variables and integrate. What do you get ? Post your work.
 
  • #4
First of all, thank you for the quick replies! I tried a u-substitution again but don't seem to get anywhere:

u = 1/x
dx = - (x^2) du

and v = - (e^u) / (u*((u^-1) + 1)^2) du

And that's as far as I get. Is there something that I am missing?
 
  • #5
Bump.

Anyone?
 
  • #6
dextercioby
Science Advisor
Homework Helper
Insights Author
12,985
540
How can you simplify the denominator ?
 
  • #7
I finally got it; this was one insane integral!

From where I left, the denominator had to be simplified and I had to do another integral (by parts) before I got the answer.

The solution was: y = [(x*exp(1/x)) / (x+1)] + k

Thanks for your help Gib Z and bigubau!
 

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