# Math Help - Homogeneous Diff Eqn's

1. ## Homogeneous Diff Eqn's

Can anyone help me with this question, please?

Find a di®erential 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: $y^2=2px$ where $p$ 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 $x$ and you get the following differential equation: $2yy'=2p$ where you can substitute $2p$ with general constant term $C$ providing the constraint $C>0$ 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!