Unable to solve the collocation equations -- a singular Jacobian encountered.

Hi, I'm trying to run the code below. However, it displays the following error message: "Unable to solve the collocation equations -- a singular Jacobian encountered". Is there any way to solve this problem? Thanks in advance.

syms y(x) x Y 
k=5/8;
w=100;
q=1;
p1=1;
r=0.06;
e=0.5;
a=1/3;
t=0.9;
s1=2;
m2=0.5;
sigma=(1-k)*(e/(1-e));
Dy=diff(y,1);
D2y=diff(y,2);
t0y=(1-a)/(e^2+a*e-a*(e^2)-2*e+1)/(r+t*p1*s1-sigma*m2-0.5*sigma*(sigma-1)*(s1^2));
ezafe=(1/(1+((1-a)/(e^2-a*e-a*(e^2)-2*e+a))))*(1/(((1-a)/(e^2-a*e-a*(e^2)-2*e+a)-Dy*x))*((1-e)*(e^2-a*e-a*(e^2)-2*e+a)/(1-e*(1-a)*(e/(1-e))*((1-a)/w*q*a)^(e/(1-e)))))^((1-a)*(1-e)/(1-e*(1-a)));
gq=((x*(r-sigma*m2-0.5*sigma*(sigma-1)*(s1^2)+(sigma^2)*(s1^2)-ezafe)));
ode=y-(((1-a)/(e^2+a*e-a*(e^2)-2*e+1))+t*p1*Dy*sigma*x*s1+0.5*D2y*(x^2)*(sigma^2)*(s1^2)-Dy*x*(sigma^2)*(s1^2)+Dy*gq)/(r+t*p1*sigma*s1-sigma*m2-0.5*sigma*(sigma-1)*(s1^2));
[VF,Subs] = odeToVectorField(ode);
odefcn = matlabFunction(VF, 'Vars',{x,Y});
bcfcn = @(ya,yb)[ya(1)-t0y;yb(1)];
xmesh = linspace(0.001,450,10);
solinit = bvpinit(xmesh, [1 1]);
sol = bvp4c(odefcn,bcfcn,solinit);

Answer 1

[Star Strider]

Your ‘odefcn’ has a divide-by-zero somewhere, since at x=0, ‘Y(2)’ is NaN, and setting ‘x’ to something greater than 0 ‘Y(2)’ is Inf, even with ‘Y’ initially set to [1 1].

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