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Re: How to find the roots of non linear equations
Posted:
Mar 5, 2013 4:16 AM
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Multiple equations need to be entered as a list
f1 = a*Sin[x]/l0 + b*Sin[x]/l1; f2 = y*Cos[x]/l0 + y*Cos[x]/l1 - (1/e^y); soln1 = Solve[{f1 == 0, f2 == 0}, {x, y}] // Simplify
Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>
{{x -> -ArcCos[(-l0 - l1)/ Sqrt[(l0 + l1)^2]], y -> ProductLog[ -((l0*l1*Log[e])/ Sqrt[(l0 + l1)^2])]/ Log[e]}, {x -> ArcCos[(-l0 - l1)/ Sqrt[(l0 + l1)^2]], y -> ProductLog[ -((l0*l1*Log[e])/ Sqrt[(l0 + l1)^2])]/ Log[e]}, {x -> -ArcCos[(l0 + l1)/ Sqrt[(l0 + l1)^2]], y -> ProductLog[ (l0*l1*Log[e])/ Sqrt[(l0 + l1)^2]]/ Log[e]}, {x -> ArcCos[(l0 + l1)/ Sqrt[(l0 + l1)^2]], y -> ProductLog[ (l0*l1*Log[e])/ Sqrt[(l0 + l1)^2]]/ Log[e]}}
Verifying
{f1 == 0, f2 == 0} /. soln1 // Simplify
{{True, True}, {True, True}, {True, True}, {True, True}}
Or if the denominators are intended to be the numbers 10 and 11 and e is intended to be E
f1 = a*Sin[x]/10 + b*Sin[x]/11; f2 = y*Cos[x]/10 + y*Cos[x]/11 - (1/E^y); soln2 = Solve[{f1 == 0, f2 == 0}, {x, y}]
Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>
{{x -> -Pi, y -> ProductLog[ -(110/21)]}, {x -> Pi, y -> ProductLog[-(110/21)]}, {x -> 0, y -> ProductLog[ 110/21]}}
Verifying
{f1 == 0, f2 == 0} /. soln2 // Simplify
{{True, True}, {True, True}, {True, True}}
Bob Hanlon
2013/3/3 Norman Polozka <normanmath@gmail.com>: > 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}] >
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