# Supposedly simple calculus problem.

1. Nov 2, 2011

### Darth Frodo

1. The problem statement, all variables and given/known data

Solve the differential equation.

$\frac{dy}{dx}$ = $\frac{1}{xy}$ + $\frac{y}{x}$

3. The attempt at a solution

$\frac{dy}{dx}$ = $\frac{x + xy^{2}}{x^{2}y}$

$\frac{dy}{dx}$ = ($\frac{x}{x^{2}}$)($\frac{1 + y^{2}}{y}$)

($\frac{y}{1 + y^{2}}$)dy = $\frac{x}{x^{2}}$dx

$\oint\frac{y}{1 + y^{2}}$dy = $\oint\frac{x}{x^{2}}$dx

I can't seem to get any further than there

Last edited: Nov 2, 2011
2. Nov 2, 2011

### lurflurf

change variables u=y/x

3. Nov 2, 2011

### Staff: Mentor

It's simpler to just factor out 1/x, giving
dy/dx = (1/x)(1/y + y) = (1/x)(1 + y2)/y
The first integral can be done with an ordinary substitution. In the integral on the right, simplify x/x2.

4. Nov 2, 2011

### Ray Vickson

Try multiplying both sides of your original DE by y.

RGV

5. Nov 2, 2011

### Staff: Mentor

Guys, the equation is separable, and the OP is close to getting a solution. IMO, the best thing to do is help him along the path he's on (which is the simplest), rather than steering him in a different direction.

6. Nov 2, 2011

### Ray Vickson

I could not see the rest of his submission on my i-phone at the coffee shop, so that's why I replied.

RGV