Solving Parachute Problem: General Equation of Parabola to Differential Equation

[Blankman013]

Ok, I am pretty much out of ideas, throwing up a hail mary looking for some help here, lol.


General equation of a parabola is x(y)=ay^2+by+c, i need x(0)=10 and x(5)=0.
So C must equal 10, and b=-2-5a. So the equation is now x(y)=ay^2-(2+5a)y+10.

Now, from here i must somehow derive the differential equation
(d^2y/dt^2)+(g/(1+(2ay-(2+5a))^2))=0 with y(0)=5 and y'(0)=0.

g=10m/s^2

I know the denominator is the same as 1+(x'^2), but apparently i have no idea how to derive differential equations. So thank you for any help! I have more information on the problem but I'm not sure what else would be needed for the derivation.

 

[HallsofIvy]

Are you not given more information? Given one function, there exist an infinite number of differential equations it could satisfy! How are you supposed to pick out that particular differential equation? In particular, there is no "g" in your original function, so how could you know that it should appear in the equation?

Showing that a function does satisfy a particular differential equation, on the other hand, is relatively simple.