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

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

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

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

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.
…
$$y=1/(1-ln|x|)$$
Therefore, i find intervals $$(\infty, e), (0,e), (- \infty , -e)$$ where y(x) is defined.

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

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 …