Help with Integration Step in y'=1+0.01y^2 Problem - Expert Advice

  • Thread starter Thread starter asdf1
  • Start date Start date
  • Tags Tags
    Integration Stuck
Click For Summary

Homework Help Overview

The problem involves the differential equation y' = 1 + 0.01y^2, where participants are discussing the integration step necessary to solve it.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to separate variables and integrate, but expresses difficulty at the integration step. Another participant suggests a transformation that leads to a potential arctangent function, prompting further discussion about this approach.

Discussion Status

Participants are engaging with the integration process, with one offering a transformation that hints at a known integral form. There is a light-hearted exchange regarding the arctangent function, indicating a collaborative atmosphere without a definitive conclusion reached yet.

Contextual Notes

There is an indication of a missing step in the integration process, and participants are reflecting on their recollections of integral forms related to arctangent.

asdf1
Messages
734
Reaction score
0
In the problem, y`= 1+0.01y^2
the first i took was
dy/(1+0.01y^2)=dx
however, I'm stuck on the integration step...
can someone help?
 
Physics news on Phys.org
[tex]\int {\frac{{dy}}{{1 + 0.01y^2 }}} = \int {\frac{{dy}}{{1 + \left( {\frac{y}{{10}}} \right)^2 }}} = 10\int {\frac{{d\left( {\frac{y}{{10}}} \right)}}{{1 + \left( {\frac{y}{{10}}} \right)^2 }}}[/tex]

The last one smells arctan-ish :smile:
 
jeepers! thanks for reminding me about the arctan-ish thingy...
crud, totally forgot about that one~
:)
 
No problem; but never forget the arctan hehe :biggrin:
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
10K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
25
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
6
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
5
Views
2K