# Differential Equation first order help

#### mlazos

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

Homework Helper
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

Homework Helper
Gold Member
Dearly Missed
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).

#### mlazos

you are right,
the answer was obvious.i guess i need to rest a little. thank you guys.

Last edited:

#### arildno

Homework Helper
Gold Member
Dearly Missed
As a hint, you ought to rewrite the left-hand side as:
$$\frac{rdr}{\sqrt{cr^{2}+br+a}}=\frac{dr}{2c}(\frac{2cr+b}{\sqrt{cr^{2}+br+a}}-\frac{b}{\sqrt{cr^{2}+br+a}})$$

#### StatusX

Homework Helper
Sorry, I thought that was d^2/dt^2.

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