You have two fairly complicated equations, in two unknowns. Why do you expect an analytical solution to exist at all? I'd have been utterly surprised if one did. It is better if you just subtract the constant right hand side, because now you can plot the surfaces.
A = (131072*29284206217013915^(1/2))/(625*(((6987459706243381*W - (6987459706243381*W - ((188416*(9223372036854775808*W - 5856841243402783)^2)/12869035935211193115234375 + (1184898369045330659387084111872*2^(1/2))/(87890625*((2305843009213693952*W + 17570523730208349)/W)^(1/2)) + 1343418817046756753408/87890625)/log(((2305843009213693952*W^2)/5856841243402783 + 127/25000)/W))/((5856841243402783*tanh((73786976294838206464*s)/5856841243402783)*exp(-exp(233/100 - (583378281331064569856*W)/146421031085069575)/10))/(9223372036854775808*s) + 1) + ((188416*(9223372036854775808*W - 5856841243402783)^2)/12869035935211193115234375 + (1184898369045330659387084111872*2^(1/2))/(87890625*((2305843009213693952*W + 17570523730208349)/W)^(1/2)) + 1343418817046756753408/87890625)/log(((2305843009213693952*W^2)/5856841243402783 + 127/25000)/W))*(191916973863822393344*tanh((73786976294838206464*s)/5856841243402783) + 604462909807314587353088*s*exp(exp(233/100 - (583378281331064569856*W)/146421031085069575)/10) + 48167231430905666015625*W*log(((2305843009213693952*W^2)/5856841243402783 + 127/25000)/W)*tanh((73786976294838206464*s)/5856841243402783)))/(log(((2305843009213693952*W^2)/5856841243402783 + 127/25000)/W)*(5856841243402783*tanh((73786976294838206464*s)/5856841243402783) + 9223372036854775808*s*exp(exp(233/100 - (583378281331064569856*W)/146421031085069575)/10))))^(1/2)) - sym('82.9367');
B = 4848604884312330996192171599799452960064720961461794373632/(390625*((30197372856938873356783865240544523007076102631740932096*W + 1196803464977447626879572441392246924444885789442048*log(2*(2*W + s)^(1/2) + 2*2^(1/2)*W^(1/4)*(W + s)^(1/4)) + 1196803464977447626879572441392246924444885789442048*log(1/((2*W + s)^(1/2) - 2^(1/2)*W^(1/4)*(W + s)^(1/4))) + 12207395342769963168946347226992069644318890998628352*log(coth((50000*s*pi)/127)) - ((31721688620111212543053501011329024*(9223372036854775808*W - 5856841243402783)^2)/501342689882353 + (80464336588145820923004586700794002638127030245202533672503105028096*W^(1/2))/(1953125*(576460752303423488*W + 4392630932552087)^(1/2)) + 66056980683050248153209450614638153187005796318183424)/(log(W) - log((2305843009213693952*W^2)/5856841243402783 + 127/25000)) - ((715913401141667049096758589128704*W + ((133952*(9223372036854775808*W - 5856841243402783)^2)/89296875 + (28614490977577140881519611179794734764726943744*W^(1/2))/(29296875*(576460752303423488*W + 4392630932552087)^(1/2)) + 1566065959909660640395860639744)/(log(W) - log((2305843009213693952*W^2)/5856841243402783 + 127/25000)))*(27153607276500459978752*s + 1112053888018253184))/s)*(227645271101905578581467981701973076307609129058304*W + 92026410225101700192114242347788464628541947904*log(2*(2*W + s)^(1/2) + 2*2^(1/2)*W^(1/4)*(W + s)^(1/4)) + 92026410225101700192114242347788464628541947904*log(1/((2*W + s)^(1/2) - 2^(1/2)*W^(1/4)*(W + s)^(1/4))) + 92026410225101679909704638696118040681290661888*log(coth((50000*s*pi)/127)) - 43872128685689108753488251272750948277693341237248/(5859375*s*(log(W) - log((2305843009213693952*W^2)/5856841243402783 + 127/25000))) - 15943838407882170125382859023155862270216286202583056384/(17578125*log(W) - 17578125*log((2305843009213693952*W^2)/5856841243402783 + 127/25000)) - (9396058564731152614103031140650616447679070208*W)/(5*s)))^(1/2)) - sym('37.6092');
fA = matlabFunction(A);
fB = matlabFunction(B);
HA = fcontour(fA,[0,.00100,-.001,.001]);
HA.LevelList = 0;
HA.LineColor = 'r';
hold on
HB = fcontour(fB,[0,.00100,-.001,.001]);
HB.LevelList = 0;
HB.LineColor = 'g';
legend('A','B')
xlabel W
ylabel s
grid on
That plot enables me to find the intersection of the two level lines, and thus the solution. Remember that a contour plot can act as a graphical version of a rootfinder.
You CANNOT use solve though. You MUST use a numerical solver.
Ws = vpasolve(A,B,W,s,[.0003 .0001])
Ws =
struct with fields:
W: [1×1 sym]
s: [1×1 sym]
Ws.W
ans =
0.0003813215765050440174161487085986
Ws.s
ans =
0.00012687605236583108888940489516916
Best Answer