First order homogeneous differential equations:

Solve each differential equation or IVP.

1. $\displaystyle{\frac{dy}{dx} = \frac{y-x}{y+x}}$  solution

2. $\displaystyle{\frac{dy}{dx} = \frac{x^2+3y^2}{2xy}}$  solution

3. $\displaystyle{ -y \, dx + (x+\sqrt{xy})\, dy =0}$ solution

4. $\displaystyle{xy^2\frac{dy}{dx} = y^3-x^3, \quad y(1)=2}$  solution

5. $(x^2+y^2)dx+(x^2-xy)dy =0$   solution

6. $\displaystyle{\frac{dy}{dx} = \frac{y-4x}{x-y}}$  solution