# Separable Equation

## Homework Statement

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

## 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

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tiny-tim
Homework Helper
$$dy/dx = y^{2}/x$$
$$\int dy/y= \int dx/x$$
Hi 2RIP!

erm … what happend to the y2?

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 Helper

## 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 …