How to Nonlinear Equation?

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!

Answer 1

[Torsten]

help fsolve

Best wishes

Torsten.

[Phan]

thank you so much!

Answer 2

[Azzi Abdelmalek]

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])

[Phan]

The solve function sometimes does not work with very complex equations! Do you know any other way?

Answer 3

[Walter Roberson]

[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.

[Phan]

Thanks Buddy!