How to decide right solution

  • Thread starter supercali
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  • #1
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Main Question or Discussion Point

The problem that was given:
[tex]{\frac {d}{dx}}y \left( x \right) =2\,{\frac {x}{{x}^{2}\cos \left( y
\right) +4\,\sin \left( 2\,y \right) }}
[/tex] after doing some changes we get a bernuli that looks like this
[tex]2\, \left( {\frac {d}{dy}}x \left( y \right) \right) x \left( y
\right) =\cos \left( y \right) \left( x \left( y \right) \right) ^{
2}+4\,\sin \left( 2\,y \right)[/tex]
with the initial conditions that x=f(y) goes through (1,0) (1=x,0=y)
the solution is
[tex]\left( x \left( y \right) \right) ^{2}=-8-8\,\sin \left( y \right) +
9\,{{\rm e}^{\sin \left( y \right) }}[/tex]
for these conditions the boundry is Dy=(arcsin(ln(8/9)),pi/2) which includes the point in the initial conditions the only problem i have is i dont know how to choose the final solution for x(y) thus whether is it th possitive root or the negative one
 

Answers and Replies

  • #2
tiny-tim
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with the initial conditions that x=f(y) goes through (1,0) (1=x,0=y)

the only problem i have is i dont know how to choose the final solution for x(y) thus whether is it th possitive root or the negative one
Hi supercali! :smile:

But if it goes through (1,0), with x = 1, then it must be the positive solution, mustn't it? :confused:
 
  • #3
53
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how stupid of me how did i not notie that??????
after solving this creepy thing i must have been too exhausted :-)
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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249
:wink: fragilistic! :wink:
 

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