Dx/dt=1-1/y dy/dt=1/(x-t)

  • Thread starter raul_l
  • Start date
  • #1
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Homework Statement



dx/dt=1-1/y
dy/dt=1/(x-t)

The Attempt at a Solution



If I take the derivative of the second equation and substitute it to the first one I

[tex] \frac{d^2 y}{dt^2} - \frac{1}{y} (\frac{dy}{dt})^2 = 0 [/tex]

but I don't know how to solve this. Could anyone name any methods that could try?
Thanks.
 

Answers and Replies

  • #2
hunt_mat
Homework Helper
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The trick is to notice
[tex]
y''-\frac{1}{y}(y')^{2}=0\Rightarrow\frac{y''}{y'}=\frac{y'}{y}
[/tex]
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
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543
[tex]
y''-\frac{1}{y}(y')^{2}=0\Rightarrow yy''= y'^{2} [/tex]

Now put in the equation [itex] y=Ae^{Bt} [/itex] and find A and B.
 

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