# Differential equation

1. Feb 7, 2007

### Logarythmic

Can anyone help me solve

$$\dot{x} = Hx_0 \left( \sqrt{B} \frac{x_0}{x} + \sqrt{1-A-B} \right)$$

2. Feb 7, 2007

### mjsd

what is what? in any case, try integrating factor method

3. Feb 7, 2007

### Logarythmic

It's equivalent to solving

$$y \frac{dy}{dx} + ay + b = 0$$

4. Feb 7, 2007

### HallsofIvy

Staff Emeritus
We need more information. Are you saying that A, B, H, and x0 are constants? Is so, simplify by letting
$$U= \frac{H\sqrt{B}x_0^2}{x}$$
and
$$V= Hx_0\sqrt{1- A- B}[/itex] So your equation becomes [tex]\frac{dx}{dt}= \frac{U}{x}+ V= \frac{U+ Vx}{x}$$
$$\frac{xdx}{U+ Vx}= dt[/itex] That's easy to integrate. Last edited by a moderator: Feb 7, 2007 5. Feb 7, 2007 ### Logarythmic Then I get [tex]t= \frac{x}{V} -\frac{U}{V^2}ln(Vx+U)$$

and trying to solve this for x is rather difficult?