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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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