How to solve two simultaneous differential equations?

I have two simultaneous differential equations. Each of their solutions contain two unknown constants C1 and C2. But each of the differential equations have one boundary conditions. Now using those two boundary conditions how can I get the values of C1 and C2 in Mathematica.

You can easily do it in hand using the elimination or substitution methods on the two solutions. But I need the way to do in Mathematica for complex systems.

The first step to solving a problem like this is to create a simple example of it. Right now, I’m not sure I completely understand what you mean. Can you make a simple example of this kind of problem and show what code you would use for it?

The answer of course is to substitute actual values into the equations and then get sufficient algebraic formulas relating C1 and C2 to solve for their values. But without a concrete example, it’s hard to communicate anything concrete.