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I have the following set of equations:

1)

$\text{$b_1$} \cos (\text{$\beta_1$} u)-\text{$b_1$} \cosh (\text{$\beta_1$} u)-\text{$b2$} \cos (\text{$\beta_1$} \theta y)-\text{$d_2$} \cosh (\text{$\beta_1$} \theta y)\sin (\text{$\beta_1$} u)-\sinh (\text{$\beta_1$} u)=0$

2)

$-\text{$b_1$} \sin (\text{$\beta_1$} u)-\text{$b_1$} \sinh (\text{$\beta_1$} u)+\text{$b_2$} \theta \sin (\text{$\beta $1} \theta y)-\text{$d_2$} \theta \sinh (\text{$\beta_1$} \theta y)+\cos (\text{$\beta_1$} u)-\cosh (\text{$\beta_1$} u)=0$

3)

$-\text{$b_1$} \cos (\text{$\beta_1$} u)-\text{$b_1$} \cosh (\text{$\beta_1$} u)+\alpha ^4 \text{$b_2$} \theta ^2 \cos (\text{$\beta_1$} \theta y)-\alpha ^4 \text{$d_2$} \theta ^2 \cosh (\text{$\beta_1$} \theta y)-\sin (\text{$\beta_1$} u)-\sinh (\text{$\beta_1$} u)=0$

... and I would like to find the constants $b_1$, $b_2$ and $d_2$.

I already know the answers:

$b_1 =\frac{\sin \left(\beta _1 u\right)-\sinh \left(\beta _1 u\right)}{\cosh \left(\beta _1 u\right)-\cos \left(\beta _1 u\right)}$

$b_2 =\frac{2 \cos \left(\beta _1 u\right) \left(\cos \left(\beta _1 u\right) \cosh \left(\beta _1 u\right)-1\right)}{\theta \left(\cosh \left(\beta _1 u\right)-\cos \left(\beta _1 u\right)\right) \left(\cos \left(\beta _1 \theta y\right) \sinh \left(\beta _1 \theta y\right)+\sin \left(\beta _1 \theta y\right) \cosh \left(\beta _1 \theta y\right)\right)}$

$d_2 = -b_2 \frac{\cos \left(\beta _1 \theta y\right)}{\cosh \left(\beta _1 \theta y\right)}$

... but I want to prove it with Mathematica:

eq={b1 Cos[u β1] - b2 Cos[y β1 θ] - 
      b1 Cosh[u β1] - d2 Cosh[y β1 θ] + 
      Sin[u β1] - Sinh[u β1], 
     Cos[u β1] - Cosh[u β1] - b1 Sin[u β1] + 
      b2 θ Sin[y β1 θ] - b1 Sinh[u β1] - 
      d2 θ Sinh[y β1 θ], -b1 Cos[u β1] + 
      b2 α^4 θ^2 Cos[y β1 θ] - 
      b1 Cosh[u β1] - 
      d2 α^4 θ^2 Cosh[y β1 θ] - 
      Sin[u β1] - Sinh[u β1]}

I want to find the constants {b1, b2, d2}

Solve[# == 0 & /@ eq, {b1, b2, d2}] // Simplify

... The results are large terms and I have trouble simplifying it. Any help would be highly appreciated !

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closed as unclear what you're asking by mikado, MarcoB, Johu, José Antonio Díaz Navas, LCarvalho Oct 26 '18 at 0:40

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I would verify that the equations and solutions are consistent by substituting numerical values for all variables. $\endgroup$ – mikado Oct 5 '18 at 22:14
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    $\begingroup$ Since you believe you know the value of b1,b2,d2 then FullSimplify[expr1==0,{b1=..,b2=.., d2=..}] should have pretty good chances of returning True, but it returns b2 Cos[y β1 θ] + (1 + d2 Cosh[y β1 θ]) Sin[u β1] == 0 which tends to make me think there might be a typo or another error. If I try to do the substitutions for b1,b2,d2 the result is even worse. Are you certain no errors slipped through? I tried to carefully undo all your Latex work to get it back into MMA, but I might have made mistakes doing that too. $\endgroup$ – Bill Oct 6 '18 at 3:55
  • $\begingroup$ Because α does not appear in the solution given, it follows that b2 Cos[y β1 θ] - d2 Cosh[y β1 θ] == 0, which clearly is inconsistent with the solution for d2 in the question. I believe that there are errors in eq. $\endgroup$ – bbgodfrey Oct 6 '18 at 4:18
  • $\begingroup$ @Bill Thank you very much for your comment and your help ! Indeed this might be a mistake on my side. I will check everything again... but this might take a while. $\endgroup$ – james Oct 6 '18 at 7:15
  • $\begingroup$ @bbgodfrey Thanks for your comment. Yes, there is an error somewhere. As I have already told Bill, I will check everything again. However, this might take a while... $\endgroup$ – james Oct 6 '18 at 7:16