# Second order differential equation

1. May 26, 2013

### jtruth914

Find a solution to the following second order differential equation
xy'+y=1/y^2

My Attempt:

P= y'= dy/dx

x dy/dx + y = 1/y^2

dy/dx + y/x = 1/xy^2

Integrating Factor = e^∫1/x dx = e^lnx

y e^lnx=∫ (e^lnx)(1/xy^2) dx

2. May 26, 2013

### christoff

I do not see how this equation is second-order. Where is the second derivative of y?

So where are you stuck? What are you doing?

It bothers me a little that you seem to be using an integrating factor on a nonlinear differential equation; typically, multiplying by an integrating factor is something you do when the the DE is linear (this one isn't since you have a y^2 term).

This differential equation is nonlinear, so it must be one of the types that can be solved explicitly (if this is a homework problem). Can it be shown to be exact, homogeneous, or Bernoulli? (Hint: it can.)