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Question: How can i deal with this error

Question:How can i deal with this error

wshassanin 5 Maple
syntax 2dmath dsolve differential-equations
November 10 2019
1

I have a system of nonlinear differential equations with initial conditions:


 

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restart
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de0 := {(1-p)*(diff(f(x), x, x))+p*(beta*[5]*f(x)*(diff(f(x), x))^2+beta[11]*f(x)^7+beta[6]*(diff(f(x), x))^3+beta[7]*f(x)^5+f(x)+diff(f(x), x, x)+beta[3]*f(x)^3+beta[1]*f(x)+beta[2]*(diff(f(x), x))+mu[1]*(diff(f(x), x))+(3/4)*rho*f(x)^3+beta[9]*f(x)^2*(diff(f(x), x))^3+beta[12]*f(x)^4*(diff(f(x), x))^3+beta[13]*f(x)*(diff(f(x), x))^6+beta[10]*f(x)*(diff(f(x), x))^4+beta[8]*f(x)^4*(diff(f(x), x))+beta[4]*f(x)^2*(diff(f(x), x))-(1/4)*rho*(g(x)^3-3*f(x)^2*g(x))*sin(4*Omega*x)-alpha[2]*f(x)^3*cos(2*Omega*x)-(1/4)*rho*(3*f(x)*g(x)^2-f(x)^3)*cos(4*Omega*x)-alpha[1]*g(x)*sin(2*Omega*x)-(1/2)*alpha[2]*(f(x)^3+3*f(x)^2*g(x))*sin(2*Omega*x)+(3/4)*rho*f(x)*g(x)^2-alpha[1]*f(x)*cos(2*Omega*x)-F*Omega^2*cos(Omega*x+theta)), (1-p)*(diff(g(x), x, x))+p*(diff(g(x), x, x)+beta[11]*g(x)^7+beta[7]*g(x)^5+beta[6]*(diff(g(x), x))^3+beta[1]*g(x)+beta[2]*(diff(g(x), x))+beta[3]*g(x)^3+mu[2]*(diff(g(x), x))+(3/4)*rho*g(x)^3+g(x)+beta[9]*g(x)^2*(diff(g(x), x))^3+beta[13]*g(x)*(diff(g(x), x))^6+beta[8]*g(x)^4*(diff(g(x), x))+beta[10]*g(x)*(diff(g(x), x))^4+beta[4]*g(x)^2*(diff(g(x), x))+beta[12]*g(x)^4*(diff(g(x), x))^3+beta[5]*g(x)*(diff(g(x), x))^2-(1/4)*rho*(3*f(x)*g(x)^2-f(x)^3)*sin(4*Omega*x)+(3/4)*rho*g(x)*f(x)^2-F*Omega^2*sin(Omega*x+theta)-(1/2)*alpha[2]*(f(x)^3+3*f(x)*g(x)^2)*sin(2*Omega*x)-alpha[2]*g(x)^3*cos(2*Omega*x)-(1/4)*rho*(3*f(x)^2*g(x)-g(x)^3)*cos(4*Omega*x)-alpha[1]*f(x)*sin(2*Omega*x)+alpha[1]*g(x)*cos(2*Omega*x))}:
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ibvc0 := {f(0), g(0), (D(f))(0), (D(g))(0)}:
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n := 3:
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F := unapply(add(b[k](x)*p^k, k = 0 .. n), x):
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de := map(series, eval(de0, {f = F, g = G}), p = 0, n+1):
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for k from 0 to n do if k = 0 then ibvc := expand(eval[recurse](ibvc0, {f = F, g = G, p = 0})) else ibvc := {b[k](0)-1, (D(b[k]))(0)-1, (D(c[k]))(0)-1, ((D@@2)(b[k]))(0)-1, ((D@@2)(c[k]))(0)-1, c[k](0) = 1} end if; sys := `union`(simplify(map(coeff, de, p, k)), ibvc); soln := dsolve(sys); b[k] := unapply(eval(b[k](x), soln), x); c[k] := unapply(eval(c[k](x), soln), x) end do; 'F(x)' = F(x); 'G(x)' = G(x)

Error, (in dsolve) invalid input: `PDEtools/NumerDenom` expects its 1st argument, ee, to be of type algebraic, but received [0]

  

F(x) = b[1](x)*p+b[2](x)*p^2+b[3](x)*p^3

  

G(x) = c[1](x)*p+c[2](x)*p^2+c[3](x)*p^3

 (1)
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``


How would I deal with this error message

Download 6_11_2019_nonlinear_d_e.mw
 

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