Solve Separable Equation: Interval for y(x)

[2RIP]

Homework Statement

Solve y'=y^2/x , y(1)=1 and give the largest x-interval on which the solution y(x) is defined.

Homework Equations

The Attempt at a Solution

dy/dx = y^{2}/x
\int dy/y^{2}= \int dx/x
y=1/(1-ln|x|)<br />

Therefore, i find intervals (\infty, e), (0,e), (- \infty , -e) where y(x) is defined.

so would the intervals to choose be (\infty, e) &amp; (- \infty , -e)??

Thanks

 

[tiny-tim]

dy/dx = y^{2}/x
\int dy/y= \int dx/x

Hi 2RIP!

erm … what happened to the y²?

 

[2RIP]

Oh sorry, i was still learning how to use the latex coding and left it out. But the rest of my solution should be correct.

Thanks for pointing that out.

 

[tiny-tim]

Homework Statement

Solve y'=y^2/x , y(1)=1 and give the largest x-interval on which the solution y(x) is defined.
…
y=1/(1-ln|x|)<br />
Therefore, i find intervals (\infty, e), (0,e), (- \infty , -e) where y(x) is defined.

so would the intervals to choose be (\infty, e) &amp; (- \infty , -e)?

Hi 2RIP!

y is defined at x = 0 , isn't it?

I'm a little confused by the question … the two largest intervals are both infinite …

I suspect they mean the largest interval containing x = 1.

I'm not sure, though …