Question: over defined problem

 Have to solve and ODE in the domain of [-infnity +infinity ] via specific analytical method but due to some restrictions it could not be solved. In order to solve it, I have separated the domain into [-infinity 0 ] and [0 infinity]. So, I have to add some boundary values at x=0 to the problem. Assuming the solution of the mentioned ODE in  [-infinity 0 ] is g(x) and in [0 infinity]  is f(x), I added the boundary values of f(0)=g(0)=a and f ' (0)=b and obtained f(x) and g(x) depending on a and b.  Now I have two equations depending on the constants of a and b which have to be obtained from continuity at x=0. In other words the constants have to be determined by following relations:

 f(0)=g(0)

f ' (0)=g ' (0)

 f ' ' (0)=g ' ' (0)

f ' ' ' (0)=g ' ' ' (0)

...

As it is obvious, there are 2 unknowns and many relations. Over defined!

I think the most appropriate values of a and b are the ones which can minimize the residuals of these relations. How can MAPLE help me with this problem?

 Have to solve and ODE in the domain of [ ] via specific analytical method but due to some restrictions it could not be solved. In order to solve it, I have separated the domain into [ -] and [] so, I have to add some boundary values at x=0 to the problem. Assuming the solution of the mentioned ODE in  [ -] is g(x) and in  is f(x), I added the boundary values of   and  and obtained f(x) and g(x) depending on a and b.  Now I have two equations depending on the constants of a and b which have to be obtained from continuity law at x=0. In other words the constants have to be determined by following relations:

…

As it is obvious, there are 2 unknowns and many relations. Over defined!

I think the most appropriate values of a and b are the ones which can minimize the residuals of these relations. How can MAPLE help me with this problem?