1. Homogeneous Diff Eqn's

Can anyone help me with this question, please?

Find a diŽerential equation whose solution is the family of parabolas
with vertices and foci on the
x-axis.

2. Everything starts from the equation of the parabola. Parabolas with vertices and foci on the abscissa all have the following equation: $\displaystyle y^2=2px$ where $\displaystyle p$ is the distance between the focus and the origin of the coordinate system (in this case its the distance along the abscissa). Applying derivative with respect to $\displaystyle x$ and you get the following differential equation:$\displaystyle 2yy'=2p$ where you can substitute $\displaystyle 2p$ with general constant term $\displaystyle C$ providing the constraint $\displaystyle C>0$ since it carries the information about the distance which cannot be negative.

Hope this helps.

3. Thanks, MathoMan! It does help. I found the answer in the book, which states that the differential equation is 2XY'=Y. Gonna try and figure out how that relates to your equation. Thanks again!