Using seperation of variables?

**punkstart** · April 19th 2010, 10:18 AM

What is the procedure or what are the steps to be carried out here:
$\frac{X\prime}{X}=\frac{1}{4}(\frac{Y}{Y\prime})=\ lambda$
The answer is given as $X=e^{\lambda\alpha}$ and $Y=e^{\frac{\beta}{4\lambda}}$
I don't know how to get to the answer, i have done seperation of variables, but not when i have a derivative as a denominator!

**AllanCuz** · April 19th 2010, 11:01 AM

Originally Posted by punkstart

What is the procedure or what are the steps to be carried out here:
$\frac{X\prime}{X}=\frac{1}{4}(\frac{Y}{Y\prime})=\ lambda$
The answer is given as $X=e^{\lambda\alpha}$ and $Y=e^{\frac{\beta}{4\lambda}}$
I don't know how to get to the answer, i have done seperation of variables, but not when i have a derivative as a denominator!

This produces 2 equations

$X^{ \prime } - \lambda X = 0$

and

$\lambda Y^{ \prime } - \frac{Y}{4} = 0$

This can become

$Y^ { \prime } - \frac{ Y }{ \lambda 4} = 0$

To solve both,

let $X=e^{rx}$

let $Y=e^{qy}$

Therefore the first equation becomes

$re^{rx} - \lambda e^{rx} = 0$

$r= \lambda$

Hence,

$X=C_1 e^{ \lambda x }$

Of course the co-efficient is just a constant to represent the general solution. Which can be re-written in the form that they gave you.

The same follows for the Y equation!

Thread: Using seperation of variables?

LinkBack

Thread Tools

Display

Using seperation of variables?

Similar Math Help Forum Discussions

Seperation of variables.

Seperation of Variables

seperation of variables help

seperation of variables help

Seperation of Variables

Search Tags