Differential Equation first order help

mlazos
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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
 
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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).
 
This is a separable diff.eq. You may rewrite it as:
\frac{rdr}{\sqrt{a+br+cr^{2}}}=\pm{dt}
This can be readily integrated, yielding an implicit equation for the function r(t).
 
you are right,
the answer was obvious.i guess i need to rest a little. thank you guys.
 
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As a hint, you ought to rewrite the left-hand side as:
\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}})
 
Sorry, I thought that was d^2/dt^2.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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