1. ## differential equations

Solve the following differential equations.

y' = ((y^2)+xy)/(x^2)

Whats the method of solving this? What theorem am i using?

2. First divide by $y^2$ both sides : $
\tfrac{{y'}}
{{y^2 }} = \tfrac{1}
{{x^2 }} + \tfrac{1}
{x} \cdot \tfrac{1}
{y}
$

But note that: $
\tfrac{{y'}}
{{y^2 }} = - \left( {\tfrac{1}
{y}} \right)^\prime
$

Let: $
\tfrac{1}
{y} = z
$
we have: $
- z' = \tfrac{1}
{{x^2 }} + \tfrac{1}
{x} \cdot z
$

You can solve this last one by the integrating factor method

3. Why do you divide by Y^2?

4. $\frac{y^{2}+xy}{x^{2}}=\bigg( \frac{y}{x} \bigg)^{2}+\frac{y}{x}.$

Then let $y=xz.$