Solving 2nd order ODE with ODE45

Getting errors when trying to solve the following ODEs

I was following this method https://au.mathworks.com/help/symbolic/solve-differential-equation-numerically-1.html

My code

syms y1(t)
syms y2(t)
u=0.012277471;
D1=(((y1+u)^2)+(y2^2))^(3/2);
D2=(((y1-(1-u))^2)+(y2^2))^(3/2);
[V]=odeToVectorField(diff(y1, 2) ==y1+2*diff(y2)-((1-u)*(y1+u)/D1)-u*((y1-(1-u))/D2),...
    diff(y2, 2)==y2-2*diff(y2)-(1-u)*(y2/D1)-u*(y2/D2)); %converting 2nd order differential equations to 1st order

M = matlabFunction(V); %Converting symbolic expression to function handle
tspan=[0 17.065216560];
%     y1(0)   y1'(0)    y2(0)      y2'(0)
yo=[  0.994,   0,      0,     -2.001585106];

sol = ode45(M,tspan,yo)

My outputs

Error using symengine>@(Y)[Y(2);1.0./(Y(1).^2+(Y(3)+1.2277471e-2).^2).^(3.0./2.0).*Y(1).*(-9.87722529e-1)+Y(1)-Y(2).*2.0-1.0./((Y(3)-9.87722529e-1).^2+Y(1).^2).^(3.0./2.0).*Y(1).*1.2277471e-2;Y(4);-1.0./(Y(1).^2+(Y(3)+1.2277471e-2).^2).^(3.0./2.0).*(Y(3).*9.87722529e-1+1.212673470584416e-2)+Y(2).*2.0+Y(3)-1.0./((Y(3)-9.87722529e-1).^2+Y(1).^2).^(3.0./2.0).*(Y(3)-9.87722529e-1).*1.2277471e-2]
Too many input arguments.

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

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

Answer 1

[Bjorn Gustavsson]

Dont bother with the hassle to go through symbolic-variables and ode2vectorfield when transforming your 2 clean 2nd-order ODEs. Convert them by hand!

function dy12dt = myODE(t,y,mu)
y1 = y(1);
y2 = y(2);
dy1dt = y(3);
dy2dt = y(4);
D1 = ((y1+mu)^2 + y2^2)^(3/2);
d2y1dt2 = y1 + 2*dy2dt + (1-mu)*(y1+mu)/D1;
% ...and so on for d2y2dt2
dy12dt = [dy1dt;dy2dt;d2y1dt2;d2y2dt2]
end

Then you have a system of four coupled first-order ODEs to solve with ode45 with time-span and initial conditions of your choice...

HTH

[Bjorn Gustavsson]

@Torsten: What did I mess up this time?

Answer 2

[Torsten]

M = matlabFunction(V,'vars', {'t','Y'})