Third Order Boundary Value Problem (BVP) with Boundary Coditions only in Terms of Derivatives

I need to solve the boundary value problem (related to flow of fluids in conical ducts):

Y''' + 1 - Y'^2 = 0

with all the three BCs bing only on the derivatives of Y (and none on Y itself):

Y'(0)=Y"(inf)=0

Y'(inf)=1

By formulating the problem exactly as suggested here:

https://de.mathworks.com/matlabcentral/answers/52075-solving-a-third-order-non-linear-ode-using-ode45

dYdX = @(X,Y) [Y(2);  Y(3);  Y(2).^2-1];  % Differential equation
res = @(ya,yb) [ya(2);  yb(3);  yb(2)-1];   
SolYinit = bvpinit([0 5], [0; 0; 0]);
Fsol = bvp4c(dYdX, res, SolYinit);
X = Fsol.x;
Y = Fsol.y;

I tried to solve the problem, but received the Jacobian error.

Is it possible that the error is generated because the BCs do not contain Y(...), and is there a way around his problem?

[darova]

You don't have any starting position (x initial). The problem is because of this

[Saeid]

X(initial)=0 is given in

SolYinit = bvpinit([0 5], [0; 0; 0]);

Or what else do you mean?

[darova]

I mean this

Y'(0)=Y"(inf)=0

Y'(inf)=1

res = @(ya,yb) [ya(2);  yb(3);  yb(2)-1];   

THere are only derivatives. There should be at least one Y(0) or Y(inf) (starting or final position)

[Saeid]

That's what I suspected, thanks! Then I guess the way the problem is posed in the original literature source is not right.