Re: How to find the roots of non linear equations

• To: mathgroup at smc.vnet.net
• Subject: [mg120029] Re: How to find the roots of non linear equations
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Tue, 5 Mar 2013 22:13:41 -0500 (EST)
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```f1=a*Sin[x]/l0 + b*Sin[x]/l1
f2= y*Cos[x]/l0+ y*Cos[x]/l1 - (1/e^y)
Solve[f1==0,f2==0,{x,y}]

f1 = a*Sin[x]/l0 + b*Sin[x]/l1;
f2 = y*Cos[x]/l0 + y*Cos[x]/l1 - (1/e^y);
Solve[{f1 == 0, f2 == 0}, {x, y}]

{{x -> -ArcCos[-(l0/Sqrt[(l0 + l1)^2]) - l1/Sqrt[(l0 + l1)^2]],
y -> ProductLog[-((l0 l1 Log[e])/Sqrt[l0^2 + 2 l0 l1 + l1^2])]/
Log[e]}, {x ->
ArcCos[-(l0/Sqrt[(l0 + l1)^2]) - l1/Sqrt[(l0 + l1)^2]],
y -> ProductLog[-((l0 l1 Log[e])/Sqrt[l0^2 + 2 l0 l1 + l1^2])]/
Log[e]}, {x -> -ArcCos[
l0/Sqrt[(l0 + l1)^2] + l1/Sqrt[(l0 + l1)^2]],
y -> ProductLog[(l0 l1 Log[e])/Sqrt[l0^2 + 2 l0 l1 + l1^2]]/
Log[e]}, {x -> ArcCos[l0/Sqrt[(l0 + l1)^2] + l1/Sqrt[(l0 + l1)^2]],
y -> ProductLog[(l0 l1 Log[e])/Sqrt[l0^2 + 2 l0 l1 + l1^2]]/
Log[e]}}

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu

```

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