How to Nonlinear Equation?
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Dear all,
I have two non-linear equation with variable h and x:
h^2*((4*x)/exp(x^2) - 1/2)+ (2*h*x)/(x^4 + 1)=0
2*h*(4/exp(x^2) - (8*x^2)/exp(h^2))=0
Does anyone know how to solve them?
Thank you so much!
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Azzi Abdelmalek
am 9 Jul. 2015
syms h x
eq1=h^2*((4*x)/exp(x^2) - 1/2)+ (2*h*x)/(x^4 + 1),
eq2=2*h*(4/exp(x^2) - (8*x^2)/exp(h^2))
sol=solve([eq1,eq2])
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Walter Roberson
am 12 Jul. 2015
[h;x] = [
-.5002995248, -.9581351468, 2.191580534, -1.788893598;
-.6491362168, .8076085058, 1.734489059, 1.370112302 ]
also, h = 0 together with any x
Solution mechanism: solve eq1 for h. Take the non-trivial root and substitute it in to eq2. solve for all solutions. I used Maple's allvalues() on the RootOf() that resulted from solve(), but you could use the techniques outlined in vpasolve(). Back-substitute those x values into the solution for h found in the first step.
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