Use ode45(). this ODE can be written as a system of 3 first-order ODEs
odeFun = @(t, y) [y(2);
y(3);
((3*y(2).*y(3).^2)./(y(2).^2 + 1).^(5/2) + 1./y(1).^3 - 1/y(1).^2 + 3).*((y(2).^2 + 1).^(3/2))];
tspan = [0 1];
ic = [1.1; 17.1; 144.1];
[t, y] = ode45(odeFun, tspan, ic);
plot(t, y);
However, it seems that the ODE is unstable, and the solution diverges to infinity. You may check if the equation is written correctly.
