Ordinary Differential Equation

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October 23rd 2007, 06:17 AM
Unoticed

Ordinary Differential Equation

I've been looking at this for a while, I don't really know where to start. The question is: what is the general solution to the following ordinary differential equation:

dy/dx = √(4x+2y-1)

Any help would be appreciated.
October 23rd 2007, 06:26 AM
ThePerfectHacker

Quote:

Originally Posted by Unoticed

I've been looking at this for a while, I don't really know where to start. The question is: what is the general solution to the following ordinary differential equation:

dy/dx = √(4x+2y-1)

Any help would be appreciated.

$y ' = \sqrt{4x+2y-1}$
Let $z=4x+2y-1$ then $z'=4+2y'\implies y' = \frac{1}{2}z' -2$ .
Substitute to get,
$\frac{1}{2}z' - 2 = \sqrt{z}$
That is Bernoulli Equation.
October 23rd 2007, 06:36 AM
Unoticed

Thanks a lot mate
October 23rd 2007, 07:35 AM
Unoticed

Hey, I've looked at some stuff on the Bernoulli Equation and I don't understand how to get from that to a general solution. Do I have to make another substitution?
October 23rd 2007, 08:19 AM
Krizalid

Actually, the equation is separable.
October 23rd 2007, 09:24 AM
Unoticed

really? how so? thats the first thing I tried but I couldnt get it

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