How can i get analytical solution

I can't use ode45 or dsolve

this is the Question we are given

my code (sorry for not adding any comments)

clear

%PARAMETERS
m = 8000; %kg
v = 80; %m/s
r = 250; %m
gravity = 9.81; % m/s^2
%rate_of_turn = ((2*pi)/time);
%t_360 = 2*(((pi)*turn_radius)/speed);
t_180=(pi*r)/v;
dt=0.001;

t=0:dt:t_180;
x=zeros(1,length(t));
y=zeros(1,length(t));
dVx = zeros(1,length(t));
dVy= zeros(1,length(t));

x(1) = 0;
y(1)=0;
Velcoity_x(1) =0;
Velocit_y(1)=0;

F= (m*(v^2))/r;
for i=2:length(t)
    angle(i)=angle(i-1) +t_180*dt;
    
    Velcoity_x(i)=v*cos(angle(i));
    Velocit_y(i)=v*sin(angle(i));
    
    dx(i)=Velcoity_x(i)*dt;
    dy(i)=Velocit_y(i)*dt;
    x(i)=x(i-1)+dx(i);
    y(i)=y(i-1)+dy(i);
    
    dVx(i)=(Velcoity_x(i)-Velcoity_x(i-1))/dt;
    dVy(i)=(Velocit_y(i)-Velocit_y(i-1))/dt;
    
    Force_x=dVx(i)*m;
    Force_y=dVy(i)*m;
    F(i)=((Force_x^2)+(Force_y^2))^0.5;
end

plot(x,y)
grid on

please help

Answer 1

[Walter Roberson]

You get an analytic solution by working through the calculas on paper.

By definition a numeric solution is never an analytic solution, so no numeric approach can ever find the analytic answer.

That leaves you with the choice of working it out by hand on paper (or equivalent), or else of using symbolic software such as dsolve(). But your other question says you are not permitted to use dsolve(), so that leaves you using paper (or equivalent)