Solving non-linear SECOND ORDER ODE BY MATLAB

As attached I have a nonlinear ode with boundary conditions. What I knew is my problem is a boundary value problem,but my function has a two regions

. My needed is to solve this function numercially and match the solution in the two regions.One thing has to mentioned is that this problem is a stiff problem.What solver I need to use to solve this problem and do I need to break my function into two functions of first order or not?

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Star Strider]

All the information you need is in Numerical Integration and Differential Equations (link).

[Mohammed]

Thanks

Answer 2

[Torsten]

Use "bvp4c" with its option for "Multipoint Boundary Value problems":

https://de.mathworks.com/help/matlab/ref/bvp4c.html#bt5uooc-23

Best wishes

Torsten.