Help with a Differential Equation

• Jan 23rd 2009, 09:46 AM
boredaxel
Help with a Differential Equation
How to go about solving this differential equation? I tried substitution and could not get any meaningful form of it.

x + y + 1 + (−x + y − 3)y' = 0
• Jan 23rd 2009, 09:50 AM
Jester
Quote:

Originally Posted by boredaxel
How to go about solving this differential equation? I tried substitution and could not get any meaningful form of it.

x + y + 1 + (−x + y − 3)y' = 0

Here you want to intoduce new variables $x = u + a,\;\;\;y = v + b$

such that your new equation becomes

$u + v + ( -u + v) v' = 0$ (homogeneous).

So find $a\;\;\text{and}\;\;b$ that makes this work.
• Jan 24th 2009, 01:54 AM
boredaxel
Pardon me but I still cant see how I can solve the homogeneous DE. I cant find a way to separate the variables u and v.
• Jan 24th 2009, 03:36 AM
mr fantastic
Quote:

Originally Posted by boredaxel
Pardon me but I still cant see how I can solve the homogeneous DE. I cant find a way to separate the variables u and v.

You were told the type of DE it is .... To make it more explicit, your DE can be written as:

$\frac{dv}{du} = \frac{u + v}{u - v} = \frac{1 + \frac{v}{u}}{1 - \frac{v}{u}}$.

It should be clear what to do now. A similar problem is here: http://www.mathhelpforum.com/math-he...eneous-de.html
• Jan 24th 2009, 05:57 AM
boredaxel
(Surprised) !! Thanks for all the help. I understand what to do now.