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