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Question: solve a nonlinear equation

Question:solve a nonlinear equation

mehdi jafari 769 Maple
dsolve differential-equations bvp
November 28 2020
1

i have a nonlinear equation,W, which have two unknowns: x and b 
i want to solve W for b, and the x domain is : -4e-6<x<4e-6. can anyone help? tnx in advance


 

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restart; with(DirectSearch)
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E := (-7.29511346879067*10^9*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(2.02316788462733*10^17*b+4.107030812*10^12)*phi(x)+1.74615339888993*10^17*b

(-7295113469.*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(0.2023167885e18*b+0.4107030812e13)*phi(x)+0.1746153399e18*b

 (1)
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dsolve(E, phi(x))
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ivp := {E, phi(-0.406e-3) = 1, phi(0.406e-3) = 1, (D(phi))(-0.406e-3) = 0, (D(phi))(0.406e-3) = 0}

{(-7295113469.*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(0.2023167885e18*b+0.4107030812e13)*phi(x)+0.1746153399e18*b, phi(-0.406e-3) = 1, phi(0.406e-3) = 1, (D(phi))(-0.406e-3) = 0, (D(phi))(0.406e-3) = 0}

 (2)
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N := dsolve(ivp, phi(x))
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A := simplify(rhs(dsolve(ivp, phi(x))))
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W := evalf(subs(phi(x) = simplify(rhs(dsolve(ivp, phi(x)))), (2.74505742817409*10^8+3.18054074382591*10^8*phi(x))^2-(1.63833629390402*(2.74505742817409*10^8+3.18054074382591*10^8*phi(x)))*(diff(phi(x), x, x))+3*(6.98727355657655*10^7+32282.4885498329*(diff(phi(x), x)))^2+2.68414581287153*(diff(phi(x), x, x))^2 = 0.9e17))
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