Third order BVP with non constant coefficents

Hi everyone, I'm trying to solve a third order BVP with non constant coefficents into the closed domain [a, b];

y''' = cost - (1/x)*y'' + (1/x^2)*y'

y=f(x)

with this Boundary conditions.

x=a : y=0; dy=0;

x=b : y=0;

looking into some tutorials i've found out that probably i've to transform the third order equation into a system of first order equations and then use ODE45... in another answer about a second order equation it was said that ODE45 cannot use buondary conditions given in two different points...

Can someone give me just some hints for the path to follow?

Thanks!