# Thread: Ordinary Differential Equation

1. ## 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.

2. 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.
$\displaystyle y ' = \sqrt{4x+2y-1}$
Let $\displaystyle z=4x+2y-1$ then $\displaystyle z'=4+2y'\implies y' = \frac{1}{2}z' -2$.
Substitute to get,
$\displaystyle \frac{1}{2}z' - 2 = \sqrt{z}$
That is Bernoulli Equation.

3. Thanks a lot mate

4. 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?

5. Actually, the equation is separable.

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