State four examples of partial differential equations in physics 

What is the potential difference in physics?

Define the Schwarzian derivative of a function v to be
S(v)= (v’’’÷ v’)- 3/2(v’’÷v’) ^2
a. Prove that if f and g are both solutions to y’’+q(x)y= 0 then v=f/g is a solution to the third order differential equation S(v)=2q(x)
b. As an interesting follow up suppose again that f and g are bothsolutions to y’’+q(x)y= 0. Letting v= fg, prove that v satisfiesthe second order, non-linear differential equation 2yy’’= (y’)^2-4y^2q(x)

Can someone try to explain what equations in Physics to use when doing a projectile questions? or a trajectory questions?