Re: Solving problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg32387] Re: Solving problem*From*: Erk Jensen <Erk.Jensen at cern.ch>*Date*: Fri, 18 Jan 2002 00:17:32 -0500 (EST)*References*: <a25uuu$dk4$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Nicolas Le Roux wrote: > > I have to solve a system of 4 equations with 4 variables. The problem is > that one of a variable is a born(?) of an integrale and so Mathematica > could not know whether or not the integrale is convergent. If you could > help me to solve this system, it would really help me. > You'll find the worksheet at www.via.ecp.fr/~genji/test.nb > > Thank you > > -- > Genji > "La femme ne voit jamais ce qu'on fait pour elle, elle ne voit que ce > qu'on ne fait pas." > Georges Courteline I'm not a guru, but why do you use "set delayed"? If you evaluate the integral BEFORE you try and solve the equations, you don't get the problem you encounter. However, I don't believe that you can solve the equations all analytically. What I did is \!\(eqns = Simplify[{\@\(h\^2 - e\^2\) - a*e\^2 - b\ e - c == 0, 2\ a\ e + b + \(2\ e\)\/\@\(h\^2 - e\^2\) == 0, a\ d\^2 + b\ d + c == 0, L == \[Integral]\_e\%d\(\@\( 1 + b\^2 + 4\ a\ x\ b\ + \ 4\ a\^2\ x\^2\)\) \[DifferentialD]x + h\ \((\[Pi]\/2 - ArcCos[e\/h])\)}]\) and then solved the 1st 3 equations for {a,b,c}, like Solve[eqns[[{1, 2, 3}]], {a, b, c}] // Simplify and insert the result into the forth like eq4=eqns[[4]] /. % Now you can plot the RHS - L versus e. This doesn't solve your real problem however, the function doesn't seem to be well-behaved there ... Good luck, -erk-