# Differential equation

Logarythmic
Can anyone help me solve

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

Homework Helper
Can anyone help me solve

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

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

Logarythmic
It's equivalent to solving

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

$$U= \frac{H\sqrt{B}x_0^2}{x}$$
$$V= Hx_0\sqrt{1- A- B}[/itex] So your equation becomes [tex]\frac{dx}{dt}= \frac{U}{x}+ V= \frac{U+ Vx}{x}$$
$$\frac{xdx}{U+ Vx}= dt[/itex] That's easy to integrate. Last edited by a moderator: Logarythmic Then I get [tex]t= \frac{x}{V} -\frac{U}{V^2}ln(Vx+U)$$