Solving ODE: $\dot{r}=\sqrt{\frac{a}{r}+b}$

Thread starter NoobixCube
Start date Mar 11, 2008
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Ode

In summary, an ODE, or ordinary differential equation, is an equation that describes the relationship between a function and its derivatives. To solve an ODE, one must find a function that satisfies the equation. This can be done analytically or numerically. The symbols in the ODE represent the derivative of the function, as well as constants with physical meanings. The square root in the ODE indicates the dependency of the rate of change on the square root of a function. Some real-life applications of solving ODEs include population growth, weather prediction, chemical reactions, and analyzing mechanical systems.

Mar 11, 2008

NoobixCube

Hi guys,
Could anyone suggest a method to solve this ODE w.r.t. time?
[tex]
\dot{r}=\sqrt{\frac{a}{r}+b}
[/tex]

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Mar 11, 2008

NoobixCube

I have managed to find one :redface:

1. What is an ODE?

An ODE, or ordinary differential equation, is an equation that describes the relationship between a function and its derivatives. It is commonly used to model physical phenomena in science and engineering.

2. How do you solve an ODE?

To solve an ODE, you need to find a function that satisfies the equation. This can be done analytically, using methods such as separation of variables or integrating factors, or numerically, using methods such as Euler's method or Runge-Kutta methods.

3. What is the meaning of the symbols in the ODE $\dot{r}=\sqrt{\frac{a}{r}+b}$?

The symbol $\dot{r}$ represents the derivative of the function $r$ with respect to time. The symbol $a$ represents a constant and $b$ represents another constant. These constants may have physical meanings in the context of the problem being modeled.

4. What is the significance of the square root in the ODE $\dot{r}=\sqrt{\frac{a}{r}+b}$?

The square root in this ODE indicates that the rate of change of $r$ is dependent on the square root of the function $\frac{a}{r}+b$. This can have implications on the behavior and solutions of the ODE.

5. What are some real-life applications of solving ODEs?

Solving ODEs has a wide range of applications in various fields of science and engineering. Some examples include modeling population growth, predicting weather patterns, simulating chemical reactions, and analyzing the behavior of mechanical systems.