How to use Reduce to find com

Questions
, , , , ,
1

I tried to solve the following set of equations

- v_+ = C_1 \sinh (C_2) \\ -v_+ = \sinh(-s_+ q + C_2),

where v_+, s_+ and q are constants and I try to solve for C_1 and C_2 using this code line -
Solve[-vplus == C*sinh[B] && -vplus == C*sinh[-S*q + B], {C, B}]
But I get this message -
Inverse functions are being used by Solve, so some solutions may not \ be found; use Reduce for complete solution information

How can I use Reduce here to get complete solution?

2

You wrote the equations in Latex in one form, then in the Mathematica code you used different symbols. little confusing.
Let me write your equations, and instead of using -v, just use v since it is the same. And used lowerCaseLetters. Since C is actually a Mathematica symbol. Not a good idea to use UpperCase first letter in Mathematica.
So your equations are basically these

        eq = {v == c1*Sinh[c2], v == Sinh[-s q + c2]}

To use Reduce

       Reduce[eq, {c1, c2}, Reals]

And to obtain a solution with no warnings

       Solve[eq, {c1, c2}, Reals]
3

Thank you very much for the corrections Nasser!
It does though give me a message that this equations cannot be solved with the methods available to Solve. But I don’t understand from the explanations which of the other functions can solve this type of system of equations..

4

I forgot one line. I had to convert to exponential form first and forgot to paste the line.. If you can try this. No warnings. V 10.02.

ClearAll[c1, c2, s, q];
eq = { v + c1*Sinh[c2] == 0 , v +  Sinh[-s*q + c2] == 0};
eq = TrigToExp[eq];
Reduce[eq, {c1, c2}, Reals]
Solve[eq, {c1, c2}, Reals]

6119Untitled.png
6119Untitled.png1310×511 13.5 KB