Constants from differential equations

I have a problem, I’ve solved 2 diff equations and I have:

w1[y] == (E^(β*y))*(A1*cos[β*y] +
A2*sin[β*y]) + (E^(-β*y))*(A3*cos[β*y] +
A4*sin[β*y])

w2[y] == (E^(-β*y))*(A5*cos[β*y] + A6*sin[β*y])

I have also 6 equations to find constants A1-A6 :

w1”[0] == 0, w1”'[y] == -q*L , w1[L] == w2[L], w1′[L] == w2′[L],
w1”[L] == w2”[L], w1”'[L] == w2”'[L]

How should I write it so I can find constants?
Thanks for any help

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Kuba, could You possibly help me ?
– Peter
Apr 26 ’15 at 18:16

  

 

Could You, please paste any link to example of smilar Solve use?
– Peter
Apr 26 ’15 at 18:23

  

 

Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the faq! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign!
– Michael E2
Apr 26 ’15 at 18:51

  

 

You can format inline code and code blocks by selecting it and clicking the {} button above the edit window. The edit window help button ? is also useful for learning how to format your questions and answers.
– Michael E2
Apr 26 ’15 at 18:51

  

 

@Peter Please take a tour.
– Kuba
Apr 28 ’15 at 7:17

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1 Answer
1

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Correct sin/cos to Sin/Cos. Define your functions properly: w1[y_] :=…. Then put your conditions to Solve and done.

w1[y_] := (E^(β*y))*(A1*Cos[β*y] + A2*Sin[β*y]) + (E^(-β*y))*(A3*Cos[β*y] +
A4*Sin[β*y]);

w2[y_] := (E^(-β*y))*(A5*Cos[β*y] + A6*Sin[β*y]);

vars = Symbol[“A” <> ToString[#]] & /@ Range[6]

{A1, A2, A3, A4, A5, A6}

Solve[
{w1”[0] == 0, w1”'[y] == -q*L, w1[L] == w2[L], w1′[L] == w2′[L],
w1”[L] == w2”[L], w1”'[L] == w2”'[L]},
vars
]