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Solve system of non linear equations?

pls, help me in solving the equations, which I attached. TIA

m1 = (1 - b*m (x*Sinh[m*a] + y*Cosh[m*a]))^(-1/2);
m2 = (1 - b*m (-x*Sinh[m*a] + y*Cosh[m*a]))^(-1/2);
eqs = {2*y*Sinh[m] == c*m*(x*Sinh[m1 + m2] + y*Cosh[m1 + m2])};
Solve[eqs, {x, y}, Reals]
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POSTED BY: Moslem Uddin
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It's not a school problem, it's related to my research study. I am trying to derive the exact solution of a problem if possible, rather than solving the problem graphically or numerically.

POSTED BY: Moslem Uddin
Anonymous User
Anonymous User
Posted 5 years ago

eqs=2ySinh[m] == cm(xSinh[m3] + yCosh[m3]); Solve[eqs,x] (* appears to solve quickly for x or y not both *) x==Csch[m3] (c m y Cosh[m3] - 2 y Sinh[m])/(c m)

but with m1+n2 it does not solve for me and i have no time tonight for analyzing it.

but i observe in the above that i might have "solve x==cos(x)" or rather "solve x/y==cos(1/(x+y))" or moreso 0==y cos(1/(x+y))+x sin(1/(x+y)) situation which might be impossible except trivially, the solution may not be solvable for {x,y} (x or y), and the solution mathematica can give might be limited to expressing it in a different form (ie, with x~ ArcCos[Cos[x]]). i'd need to look further to know more.

if the above can't work for you, you can always plot and get a pseudo function for some given interval (sin cos curve) something like Interpolation[points]

POSTED BY: Anonymous User
Anonymous User
Anonymous User
Posted 5 years ago

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POSTED BY: Anonymous User
Anonymous User
Anonymous User
Posted 5 years ago

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POSTED BY: Anonymous User
Anonymous User
Anonymous User
Posted 5 years ago

after doing the below (see below), my advice would be you might have an equation with very few solutions or very many depending on variable input

my advice would be (my next step might be), despite a statement of it's being "non-linear", is you should do a linear analysis to check it over. but before doing that make certain, if this is school work, you didn't copy the problem wrong or take some mis-step and have checked the "answers".

it could be a very complex problem and require lots of analysis to show where all solutions are (given all it's radicals that may split into multiple equations) and your not stating what is constant or variable (per say), i'm unsure. i assume there's a reason you need it solved?

POSTED BY: Anonymous User
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