[SOLVED] Rearranging a differential equation

**Bud** · November 25th 2008, 07:21 AM

Hi I am supposed to "just" rearrange the following equation and at one point substitute dh/dt = A/rho with the constant A:

With the constant C and rho(i).

The result looks like this:

I cannot rearrange the 1st equation in a way that I obtain the 2nd. I assume that one has to ibntegrate at one point to get rid of the logarithm though.

Thanks in advance.

Cheers

**shawsend** · November 25th 2008, 10:46 AM

If $\rho=f(h)$ and $h=g(t)$ then $\frac{d\rho}{dt}=\frac{d\rho}{dh}\frac{dh}{dt}$ right? So if we calculate what $\frac{d\rho}{dh}$ is and multiply by the given $\frac{dh}{dt}=\frac{A}{\rho}$ , that would give us $\frac{d\rho}{dt}$ . So what is:

$\frac{d}{dh}\left\{\ln\left(\frac{\rho}{\rho_i-\rho}\right)\right\}$

You can figure that out. Then isolate the $\frac{d\rho}{dh}$ term and then just multiply by $\frac{A}{\rho}$

Thread: [SOLVED] Rearranging a differential equation

LinkBack

Thread Tools

Display

[SOLVED] Rearranging a differential equation

Similar Math Help Forum Discussions

Rearranging Differential Equation

[SOLVED] Differential Equation

[SOLVED] Differential equation

[SOLVED] Differential equation

[SOLVED] Differential Equation

Search Tags