Solving ODE45 equations in matlab without a function

I am struggling to figure out what is wrong with my code please help.

%%Numerically solving for Trajectory of the Ball in a Vacuum

clc

v0=25;

% Average football is punted at 25 m/s

theta=35;

% Chosen value for the angle of a punt

g = 9.8;

t=2.5;

t2 = 1.25;

CF = [.3 .385];

y0 = 0;

xdist = v0*cosd(35)*t;

yheight = (-.5*(g*(t2^2)))+v0*sind(theta)*t2;

% A ball punted with these variables would travel 51.2 meters horizontally

% and the max height would be 10.27 meters

x = zeros(1,2);

y0 = zeros(1,2);

t = [0 2.5];

[t,x] = ode45(@(t,x) (v0*cos(theta)*exp(-CF*t)), t, y0)

--------------------------------------

and I am receiving the errors:

Error using odearguments (line 90)

@(T,X)(V0*COS(THETA)*EXP(-CF*T)) must return a column vector.

Error in ode45 (line 115)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Answer 1

[michio]

It is stated that "The function dydt = odefun(t,y), for a scalar t and a column vector y, must return a column vector dydt" (See ode45 odefun)

 [t,x] = ode45(@(t,x) (v0*cos(theta)*exp(-CF*t))', t, y0)

(added ' at the end of the function definition) would not cause an error, but could you check if you get the expected solution?

[Walter Roberson]

I would suggest .' instead of ' as you do not want the complex conjugate transpose.

[michio]

You are right. Thanks for pointing that out.

 [t,x] = ode45(@(t,x) (v0*cos(theta)*exp(-CF*t)).', t, y0)

instead.

[Jarrod Garrett]

Actually nevermind this equation is for acceleration so this does appear to be correct. Thank you so much.