Solving Differential Equations to Finding Solutions

[Logarythmic]

Can anyone help me solve

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

 

[mjsd]

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

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

 

[HallsofIvy]

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
[tex]V= Hx_0\sqrt{1- A- B}[/itex]<br /> <br /> So your equation becomes <br /> $$\frac{dx}{dt}= \frac{U}{x}+ V= \frac{U+ Vx}{x}$$<br /> [tex]\frac{xdx}{U+ Vx}= dt[/itex]<br /> <br /> That's easy to integrate.[/tex][/tex]

 

[Logarythmic]

Then I get

$$t= \frac{x}{V} -\frac{U}{V^2}ln(Vx+U)$$

and trying to solve this for x is rather difficult?