5 4.00649105280831E+00*y1*y2+ 5.26610813156747E-01*y1-4.73964757724582E-01* y5; 7.43133120490877E+00*y2*y3**2+ 5.31324863453933E+00*y1*y2+ 4.31363490603044E+00*y2**2+ 8.06989849429520E-01*y2*y3+ 1.49987275886495E-01*y2*y4+ 3.49185128215561E-01*y1+ 1.32605295558012E-01*y2-1.04758859585902E+00*y5; 1.88743868807074E+01*y2*y3**2+ 1.02481225819107E+00*y2*y3+ 4.78801780852764E-01*y3**2-1.06428266510309E+00*y5+ 1.01454213888243E-01*y3; 6.77344896993456E-02*y2*y4+ 7.80160463417002E+00*y4**2 -1.89237063040101E+00*y5; 3.89976792151467E+00*y2*y3**2+ 1.39412684031101E+00*y1*y2+ 1.13184129248280E+00*y2**2+ 4.23487130504208E-01*y2*y3+ 7.87093928408356E-02*y2*y4+ 9.89285552709683E-02*y3**2+ 4.53284262319986E+00*y4**2+ 1.83243206921733E-01*y1+ 6.95877849581671E-02*y2+ 4.19243169406760E-02*y3-2.03370256289491E+04; TITLE : scaled chemical equilibrium of hydrocarbon combustion SCALING COEFFICIENTS : 2 -1.67599894525044E+01 -0.00000000000000E+00 2.92753020454682E+00 0.00000000000000E+00 -1.84969093088580E+01 0.00000000000000E+00 -7.63798150414614E+00 0.00000000000000E+00 -6.06570250071970E+00 0.00000000000000E+00 1.58347985028662E+01 0.00000000000000E+00 1.52420534735530E+01 0.00000000000000E+00 1.55867906790425E+01 0.00000000000000E+00 1.40951758894744E+01 0.00000000000000E+00 1.43118210742736E+01 0.00000000000000E+00 THE SOLUTIONS : 16 5 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.92128055936496E+04 1.11826992898724E+01 y2 : -4.70760063942816E-02 -4.04991018427422E-05 y5 : 1.37013424264189E+04 1.39738188217081E+00 y3 : -1.01422302049308E-01 -1.88652054449720E+02 y4 : 5.76493255946996E+01 2.93995480431725E-03 == err : 4.584E-11 = rco : 5.476E-07 = res : 7.729E-12 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.92130809591834E+04 1.11837762292716E+01 y2 : -4.70781016172068E-02 -4.05036455990043E-05 y5 : 1.37011985132098E+04 1.39711958249263E+00 y3 : -1.01426750422921E-01 -1.88641960260808E+02 y4 : -5.76486141039022E+01 -2.93906678288265E-03 == err : 4.399E-11 = rco : 5.477E-07 = res : 7.276E-12 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.92128055936496E+04 -1.11826992898724E+01 y2 : -4.70760063942816E-02 4.04991018427422E-05 y5 : 1.37013424264189E+04 -1.39738188217081E+00 y3 : -1.01422302049308E-01 1.88652054449720E+02 y4 : 5.76493255946996E+01 -2.93995480431725E-03 == err : 4.584E-11 = rco : 5.476E-07 = res : 7.729E-12 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 1.92130809591834E+04 -1.11837762292716E+01 y2 : -4.70781016172068E-02 4.05036455990043E-05 y5 : 1.37011985132098E+04 -1.39711958249263E+00 y3 : -1.01426750422921E-01 1.88641960260808E+02 y4 : -5.76486141039022E+01 2.93906678288265E-03 == err : 4.399E-11 = rco : 5.477E-07 = res : 7.276E-12 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.75054466778545E+02 2.46608514515580E+02 y2 : -3.24464616614846E+00 -4.37026691608221E+00 y5 : 1.37171302665961E+04 -2.28957496046617E+01 y3 : -5.42025858073689E+00 -1.06497034777504E+01 y4 : 5.76964295745106E+01 -2.91635645814359E-02 == err : 2.083E-12 = rco : 1.249E-04 = res : 3.733E-12 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 2.38981713102819E+02 8.21073318940323E-47 y2 : 6.64422090237807E+00 -2.13821176807376E-48 y5 : 1.36878243014970E+04 -4.85801713706358E-47 y3 : -1.07849432549813E+01 -1.88162635590491E-48 y4 : -5.76495252193579E+01 1.14928882533964E-49 == err : 2.584E-11 = rco : 2.547E-04 = res : 5.457E-12 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.53856869779712E+02 -2.12580633289596E+02 y2 : -3.75982369259928E+00 5.00397994840807E+00 y5 : 1.37110042206992E+04 1.20671776870211E+01 y3 : 4.96563893125412E+00 -9.94439056801148E+00 y4 : 5.76857692571830E+01 3.64896328475527E-03 == err : 2.584E-11 = rco : 1.736E-04 = res : 2.679E-12 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.35636611621907E+02 -3.11004468940250E+02 y2 : -2.05173528067404E+00 4.37915950564526E+00 y5 : 1.37143814801902E+04 2.74409330213757E+01 y3 : -6.85535923436421E+00 1.06605029816151E+01 y4 : -5.76676655965436E+01 -7.67093750819953E-02 == err : 4.479E-11 = rco : 1.081E-04 = res : 3.393E-12 == solution 9 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.35636611621905E+02 3.11004468940250E+02 y2 : -2.05173528067402E+00 -4.37915950564529E+00 y5 : 1.37143814801902E+04 -2.74409330213757E+01 y3 : -6.85535923436423E+00 -1.06605029816151E+01 y4 : -5.76676655965436E+01 7.67093750819955E-02 == err : 4.481E-11 = rco : 1.081E-04 = res : 3.471E-12 == solution 10 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 2.74240584868995E+02 -1.24283559019287E-49 y2 : 5.76746686323101E+00 -8.35238971903811E-53 y5 : 1.36748115150506E+04 1.33638235504610E-51 y3 : 1.15099188925743E+01 -1.51387063657566E-51 y4 : -5.76183213788255E+01 -1.30506089359971E-53 == err : 3.634E-11 = rco : 1.878E-04 = res : 3.638E-12 == solution 11 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 3.45615469814633E+02 -1.23160997841048E-47 y2 : 4.54752261736269E+00 2.84649441624819E-49 y5 : 1.36697578277809E+04 4.10536659470161E-48 y3 : 1.29555044508551E+01 -7.05609883464340E-49 y4 : 5.75628981980042E+01 8.68648530779964E-51 == err : 4.105E-11 = rco : 1.274E-04 = res : 3.251E-12 == solution 12 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : 3.06002331547060E+02 8.24798484755014E-52 y2 : 5.15797748585056E+00 4.56771312759897E-54 y5 : 1.36820338463285E+04 1.14845358636774E-52 y3 : -1.22276350872455E+01 -1.76183220635960E-53 y4 : 5.75860991578912E+01 2.34503129318697E-55 == err : 2.232E-11 = rco : 1.639E-04 = res : 3.606E-12 == solution 13 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.75054466778544E+02 -2.46608514515580E+02 y2 : -3.24464616614846E+00 4.37026691608223E+00 y5 : 1.37171302665961E+04 2.28957496046615E+01 y3 : -5.42025858073690E+00 1.06497034777503E+01 y4 : 5.76964295745106E+01 2.91635645814354E-02 == err : 1.716E-12 = rco : 1.249E-04 = res : 4.383E-12 == solution 14 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.53856869779711E+02 2.12580633289596E+02 y2 : -3.75982369259929E+00 -5.00397994840809E+00 y5 : 1.37110042206992E+04 -1.20671776870213E+01 y3 : 4.96563893125412E+00 9.94439056801145E+00 y4 : 5.76857692571830E+01 -3.64896328475550E-03 == err : 2.582E-11 = rco : 1.736E-04 = res : 2.711E-12 == solution 15 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.17502236680716E+02 2.72891792406016E+02 y2 : -2.29625327005255E+00 -5.01026279844028E+00 y5 : 1.37078680334543E+04 -1.72684979189792E+01 y3 : 6.40219016229585E+00 9.95859291329695E+00 y4 : -5.76528879627690E+01 5.80665032804691E-02 == err : 4.649E-11 = rco : 1.454E-04 = res : 4.400E-12 == solution 16 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : y1 : -1.17502236680718E+02 -2.72891792406017E+02 y2 : -2.29625327005256E+00 5.01026279844024E+00 y5 : 1.37078680334543E+04 1.72684979189795E+01 y3 : 6.40219016229584E+00 -9.95859291329699E+00 y4 : -5.76528879627690E+01 -5.80665032804696E-02 == err : 4.705E-11 = rco : 1.454E-04 = res : 4.436E-12 ==