Plot function to graph differential equations

I am trying to plot the solution to the following system but the code below plots a small circle instead of a parabola, which is the solution to the system. Can anyone explain how to plot the solution (y= f(x)) or point out any errors in the code? Thank you

tspan = [0 3 5 6]; 
y0 = [0 4 5 6];
[x,y] = ode45(@(x,y) odefcn(x,y,A,B), tspan,y0); 
plot(x,y(:,1),'-o',x,y(:,2),'-.') 

function dydx = odefcn(x,y,A,B)
  dydx = zeros(4,1);
dydx(1) = y(2);   
dydx(3)= y(4); 
dydx(2) = y(2)*sqrt(y(1)*y(1)+ (y(3)*y(3)));  %this is a system of two second order differential equations 
dydx(4) = y(3)*sqrt((y(1)*y(1)+ (y(3)*y(3))-9.81;  
end 

[darova]

Attach the original equations

[Aleem Andrew]

The original equations are: x"=x'*sqrt(x'^2+y'^2); y"=y'*sqrt(x'^2+y'^2)-9.81;

Answer 1

[Star Strider]

Use a different tspan vector.

When I run your code (using random values for ‘A’ and ‘B’, since they are not supplied), I get:

Warning: Failure at t=5.659410e-01.  Unable to meet integration tolerances without reducing the
step size below the smallest value allowed (1.776357e-15) at time t. 

With:

tspan = [0 0.5]; 

I get a plot.

Also, ‘dx(4)’ as posted is missing a couple parentheses. This corrected version works:

dydx(4) = y(3)*sqrt((y(1)*y(1))+ (y(3)*y(3)))-9.81;  

Be sure that is the syntax you intended.

[Aleem Andrew]

Thank you for your response Can you explain what the initial conditions mean for t and y? Four values needed to be specified for y0 but I don't understand what intial conditions they correspond to

[Star Strider]

As always, my pleasure!

The initial conditions ‘y0’ set the initial values for the respective variables variables. The time vector, ‘tspan’ can be whatever you want that is compatible with the function you are integrating. If it only contains two elements, those define the initial and final limits of the integration time. If it contains more than two elements, the integrated function values will be output as corresponding to time values close to those elements.

See the ode45 documentation for a detailed description.

[Aleem Andrew]

Ok I will look into that for further details such as why the order of the values needs to be ascending Thank you

[Star Strider]

As always, my pleasure!

See the documentation section on tspan. Note that: ‘The elements in tspan must be all increasing or all decreasing.’ So they only need to be monotonic.