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
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 /> \frac{xdx}{U+ Vx}= dt[/itex]&lt;br /&gt; &lt;br /&gt; That&amp;#039;s easy to integrate.

 

[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?