You have an ODE that has a singularity at x=0. Further, solving for D2y leads to two different differential equations. You must decide which is the one you want to solve.
Thus the results below should be treated with care.
syms y Dy D2y x Y
ode = y-(1/(Dy/y+(D2y*x)/y))^2;
ode1 = solve(ode==0,D2y)
ode2 = matlabFunction(ode1(1),'Vars',{x,[y Dy]})
odefcn = @(x,y)[y(2);ode2(x,[y(1),y(2)])];
bcfcn = @(ya,yb)[ya(1)-2;yb(1)];
xmesh = linspace(1e-3,4,10);
solinit = bvpinit(xmesh, [1 1]);
sol = bvp4c(odefcn,bcfcn,solinit);
plot(sol.x,sol.x.*sol.y(1,:))
