Differential Equation first order help

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Can anybody tell me what can be the solution of this differential equation?

(dr/dt)^2=a/r^2+b/r+c
Is first order and i need some ideas about solving it
 

StatusX

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What have you tried? I'd suggest starting by multiplying both sides by dr/dt, and trying to get each side into the form d/dt(something).
 

arildno

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This is a separable diff.eq. You may rewrite it as:
[tex]\frac{rdr}{\sqrt{a+br+cr^{2}}}=\pm{dt}[/tex]
This can be readily integrated, yielding an implicit equation for the function r(t).
 
49
0
you are right,
the answer was obvious.i guess i need to rest a little. thank you guys.
 
Last edited:

arildno

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As a hint, you ought to rewrite the left-hand side as:
[tex]\frac{rdr}{\sqrt{cr^{2}+br+a}}=\frac{dr}{2c}(\frac{2cr+b}{\sqrt{cr^{2}+br+a}}-\frac{b}{\sqrt{cr^{2}+br+a}})[/tex]
 

StatusX

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Sorry, I thought that was d^2/dt^2.
 

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