# Thread: Non-linear Differencial Equation

1. ## Non-linear Differencial Equation

This one is my own, which supprizingly has a nice solution to it:

y' = y^2

2. Originally Posted by ThePerfectHacker
This one is my own, which supprizingly has a nice solution to it:

y' = y^2
This is just a Bernoulli equation:

Let z(x) = 1/y(x)

Then y = 1/z ==> y' = -z'/z^2

So
-z'/z^2 = 1/z^2

z' = -1

z(x) = -x + C

Thus
y(x) = 1/(C - x)
is the general solution.

-Dan

3. Ha ha I forgot about that.
I had a different idea.

4. Originally Posted by ThePerfectHacker
Ha ha I forgot about that.
I had a different idea.
Well then, what's your idea? (I've heard there is more than one way to skin a cat...)

-Dan

5. Originally Posted by topsquark
Well then, what's your idea? (I've heard there is more than one way to skin a cat...)

-Dan
Power series solution.

It really is quite elegant here.

6. Originally Posted by ThePerfectHacker
Power series solution.

It really is quite elegant here.
Ah! I can see that.

-Dan