# Help with diffy eqn terminal vel problem

by Ara macao
Tags: diffy, terminal
 P: 26 Hi, So m*dv/dt = mg - kv^2, where m is skydiver mass, g acceleration due to gravity, and k> 0 related to amount of air resistance. So I want to find the analytical solution for v(t), with the assumption that v(0) = 0. I went all the way to integrating it with a partial fraction, but then got an answer drastically different from what the book got. Thanks...
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,705 It's hard to answer because you didn't show us what you did or what answer you got!
HW Helper
P: 1,593
 Quote by Ara macao Hi, So m*dv/dt = mg - kv^2, where m is skydiver mass, g acceleration due to gravity, and k> 0 related to amount of air resistance. So I want to find the analytical solution for v(t), with the assumption that v(0) = 0. I went all the way to integrating it with a partial fraction, but then got an answer drastically different from what the book got. Thanks...
Tell you what Ara, how about looking up Riccati equations. Now, can your equation be put in such form? If if can, then such a prespective may allow an easier approach to its solution.