Calculus problem

  • Thread starter Cyannaca
  • Start date
  • #1
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Hi, I would need help on this problem. I have to solve this equation
f'(x) + ((1 -2x)/x^2)*y = 1. I started the problem and I was stuck at
y= (x^2)*e^(1/x) * integral (e^(-1/x))/(x^2) :mad: . I have no idea how to do this so if anyone knows how, it would be really appreciated.
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
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By "do this" I presume you mean you are having trouble finding an elementary expression for

[tex]
\int \frac{e^{-1/x}}{x^2} \, dx
[/tex]

What techniques have you tried to apply?
 
  • #3
3,763
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Try a substitution , realizing that (1/x²)dx = - d(1/x)

regards
marlon
 
  • #4
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(1/x²)dx = - d(1/x). Thanks a lot, I was quite lost (trying to integrate by parts...)but I finally solved it. Thanks.
 
  • #5
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For integration by parts, try ILATE (I = Inverse Trig, L = Logarithmic, A = Algebraic, T = Trig, E = Exponential). This pretty much sums up the order in which the first function should be chosen if you wish to integrate something of the form,

[tex]\int udv = uv - \int v du[/tex]

(ie--how to chose u).

Adios
Vivek
 
  • #6
Zurtex
Science Advisor
Homework Helper
1,120
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Erm, have you thought about what the derivative of:

[tex]e^{\frac{-1}{x}}[/tex]

is? I think that will solve your problem :wink:

Edit: Sorry, missed that you had solved it.
 

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