Can You Help Solve These Complex Mathematical Equations?

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  • Thread starter Thread starter ferry2
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Discussion Overview

The discussion revolves around two complex mathematical equations that participants are attempting to solve. The focus includes both the methods for solving these equations and the potential for typographical errors in their formulation.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents two equations for resolution: a differential equation and an Euler's equation.
  • Another participant claims to have solved the second equation and provides a link to their solution, along with a specific form of the solution.
  • A different participant expresses difficulty in solving the first equation and indicates attempts without success.
  • One participant suggests there may be a typographical error in the first equation, proposing an alternative formulation.
  • Another participant introduces a substitution method for the second equation, leading to a different form of the solution while referencing the previous solution provided.
  • There is acknowledgment of the possibility of a typo in the first equation, with thanks expressed to those who contributed.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the first equation, with some expressing uncertainty about its formulation. The second equation has a proposed solution, but the discussion remains open regarding the first equation.

Contextual Notes

The discussion includes potential typographical errors in the equations presented, which may affect the approaches to solving them. The methods and solutions proposed depend on these formulations.

ferry2
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Hi, friends :smile:.

These are two equations, which were unable to resolve. Hope to help me. Note: this is not home, I just want to see how to resolve the equations. Thank answered.

[tex](2y-x+1)dx-(x-3y^2)dy=0[/tex]

Find the common solution of the Euler's eqution:

[tex](2x+1)^2y''-2(2x+1)y'+4y=0,[/tex] [tex]x>-\frac{1}{2}[/tex]
 
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Hello ferry2, I have solved your 2nd equation here:

http://www.voofie.com/content/146/how-to-solve-2x12-y--2-2x1-y-4-y-0/"

And the solution is given by:

[tex]y(x) = C_1(2x+1) +C_2 (2x+1) \ln (2x+1)[/tex]
 
Last edited by a moderator:
Thanks a lot Ross Tang! Can you tell something about first equation?
 
I tried various method in solving the 1st equation, but without any success. Sorry.
 
Hello !

May be a typo in the 1st equation ? No difficulty if (2x-y+1) instead of (2y-x+1).
2nd equation : Let t=ln(2x+1) leads to
d²y/dt² -dy/dt +y =0
y(t) = exp(t)*(a*t+b)
and y(x) according to ross_tang formula.
 
It is possible there have been a typo. Thank you both.
 

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