Solve for Escape Velocity on Mars: Differential Equation Method

[verticos]

Homework Statement

The acceleration of gravity on the surface of Mars is 0.38g. The radius of Mars is 2100 miles. Determine the velocity of a particle projected in a radial direction outward from Mars and acted upon by only the gravitational attraction of Mars by first modeling the motion into a differential equation and then solving the differential equation. Use your result to determine the velocity of escape from Mars.

Homework Equations

v^(2) = [2gR^(2) / r] + C

The Attempt at a Solution

g = 0.38
r = 2100 miles
R = ?
I don't understand the differential equation part at all. I'm confused because I'm only given 2 variables...

Any help is appreciated

 

[gneill]

Your differential equation should consist of an expression that relates the acceleration experienced by the projectile with the distance.