I assume this represents some object sinking through changing desity sea water. The following shows how you might do it, though you will need to replace my simple linear density change with whatever you think is appropriate.
tspan=0:1000;
y0 =[0 0];
[t,y]=ode45(@f,tspan,y0);
subplot(2,1,1)
plot(t,y(:,1))
grid on
xlabel('time'),ylabel('depth')
subplot(2,1,2)
plot(t,y(:,2))
grid
xlabel('time'),ylabel('speed')
function speed=f(~,y)
Cd=.16;
A=.0613;
m=82.25;
V=0.0809815;
depth = y(1);
rho = interp1([0 10000],[1030 1070], depth); %This is just a linear interpolation between two values
% Needs to be replaced with
% your own relationship.
g=9.81;
speed=[y(2); (rho*V*g/(m+V*rho))-(m*g/(m+V*rho))-((1/(2*m+V*rho)*Cd*A.*rho.*y(2).^2))];
end
