Two ODE's

  • Thread starter ferry2
  • Start date
  • #1
15
0
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]
 

Answers and Replies

  • #2
64
0
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/" [Broken]

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:
  • #3
15
0
Thanks a lot Ross Tang! Can you tell something about first equation?
 
  • #4
64
0
I tried various method in solving the 1st equation, but without any success. Sorry.
 
  • #5
798
34
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.
 
  • #6
15
0
It is possible there have been a typo. Thank you both.
 

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