Solution 1. order differential equation

[santais]

Homework Statement

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:

<br /> <br /> y&#039;(t)+p*y(t)=y(t)^2<br /> <br />

Homework Equations

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

y&#039;(x) +p(x)y = q(x)

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

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

 

[fluidistic]

It looks like a http://en.wikipedia.org/wiki/Bernoulli_differential_equation.

 

[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.