# Solution 1. order differential equation

1. Jan 9, 2012

### santais

1. The problem statement, all variables and given/known data
So I've been given an assignment to find all solutions to the differential equation as mentioned below. From what can be seen, it's a 1. order differerential equation.

The assignment is as stated:

$y'(t)+p*y(t)=y(t)^2$

2. Relevant equations

So I tried to rewrite to somehow match the general form of a 1. order differential equation:

$y'(x) +p(x)y = q(x)$

But no matter what I try, I can't get it to look somehow like it.

3. The attempt at a solution

The problem is that it equals the funktion itself raised in 2. I just have no idea how to find the solution, when that is the case. I tried to rewrite and solve it, using the general solution, but no matter what, the function itself becomes a part of the solution, which shouldn't be the case.

Been using the general solution as mentioned below:

$e^{-µ(x)} * ∫e^{µ(x)} q(x)dx$

where $µ(x) = ∫p(x)dx$

and $µ(x) = px$

2. Jan 9, 2012

### fluidistic

3. Jan 10, 2012

### HACR

"e^{-µ(x)} * ∫e^{µ(x)} q(x)dx,µ(x) = ∫p(x)dx,µ(x) = px" You said µ(x)=px, but p is a function of x, so I believe it's something else. Also I think you meant not the first order since the original diff. equ is already of first order but of first degree.