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Question: Why i can't find x&y C-point ?

Question:Why i can't find x&y C-point ?

salim-barzani 1035 Maple 2024
substitution duplicate-question
March 27 2025
4

in some equation i don't have problem but in a lot of them this problem is come up for me and i don't know how fix this issue?

> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet); declare(u(x, y, t), quiet); declare(f(x, y, t), quiet)

``

 (1)
> 

thetai := t*w[i]+y*l[i]+x
> 

eqw := w[i] = (-1+sqrt(-4*b*beta*l[i]-4*a*beta+1))/(2*beta)
> 

Bij := proc (i, j) options operator, arrow; -24*alpha*beta/(sqrt(1+(-4*b*l[j]-4*a)*beta)*sqrt(1+(-4*b*l[i]-4*a)*beta)-1+((2*l[i]+2*l[j])*b+4*a)*beta) end proc
> 

NULL
> 

theta1 := normal(eval(eval(thetai, eqw), i = 1)); theta2 := normal(eval(eval(thetai, eqw), i = 2))
> 

eqf := f(x, y, t) = theta1*theta2+Bij(1, 2)
> 

eqfcomplex := eval(eval(eval(eqf, l[2] = conjugate(l[1])), l[1] = lambda[1]+I*lambda[2]))
> 

eq17 := u(x, y, t) = 2*(diff(f(x, y, t), x))/f(x, y, t); equ := simplify(eval(eq17, eqfcomplex))

u(x, y, t) = 8*(-(1/2)*(-4*b*beta*conjugate(lambda[1]+I*lambda[2])-4*a*beta+1)^(1/2)*(1+((-(4*I)*lambda[2]-4*lambda[1])*b-4*a)*beta)^(1/2)-b*beta*conjugate(lambda[1]+I*lambda[2])+1/2-(b*(lambda[1]+I*lambda[2])+2*a)*beta)*((1/2)*t*(1+((-(4*I)*lambda[2]-4*lambda[1])*b-4*a)*beta)^(1/2)+(1/2)*t*(-4*b*beta*conjugate(lambda[1]+I*lambda[2])-4*a*beta+1)^(1/2)+conjugate(lambda[1]+I*lambda[2])*y*beta+((lambda[1]+I*lambda[2])*y+2*x)*beta-t)/((1+((-(4*I)*lambda[2]-4*lambda[1])*b-4*a)*beta)^(1/2)*(-(-4*b*beta*conjugate(lambda[1]+I*lambda[2])-4*a*beta+1)^(1/2)*((2*y*((lambda[1]+I*lambda[2])*y+x)*beta+t*(b*t-y))*conjugate(lambda[1]+I*lambda[2])+2*x*((lambda[1]+I*lambda[2])*y+x)*beta+((b*(lambda[1]+I*lambda[2])+2*a)*t-(lambda[1]+I*lambda[2])*y-2*x)*t)+4*(I*lambda[2]-conjugate(lambda[1]+I*lambda[2])+lambda[1])*((1/2)*conjugate(lambda[1]+I*lambda[2])*b*y*beta+(a*y-(1/2)*b*x)*beta+(1/4)*b*t-(1/4)*y)*t)-4*t*(-4*b*beta*conjugate(lambda[1]+I*lambda[2])-4*a*beta+1)^(1/2)*(conjugate(lambda[1]+I*lambda[2])*(beta*(-y*((1/2)*b*(lambda[1]+I*lambda[2])+a)+(1/2)*b*x)-(1/4)*b*t+(1/4)*y)+(((I*lambda[1]*lambda[2]+(1/2)*lambda[1]^2-(1/2)*lambda[2]^2)*b+a*(lambda[1]+I*lambda[2]))*y-(1/2)*(lambda[1]+I*lambda[2])*b*x)*beta+(1/4)*(b*t-y)*(lambda[1]+I*lambda[2]))+4*y*beta*b*conjugate(lambda[1]+I*lambda[2])^2*(-((lambda[1]+I*lambda[2])*y+x)*beta+(1/2)*t)+conjugate(lambda[1]+I*lambda[2])*(-4*beta^2*(y^2*(b*(lambda[1]^2-lambda[2]^2+(2*I)*lambda[1]*lambda[2])+2*a*(lambda[1]+I*lambda[2]))+2*x*(b*(lambda[1]+I*lambda[2])+a)*y+b*x^2)+2*beta*(-4*b*(b*(lambda[1]+I*lambda[2])+a)*t^2+2*t*(y*(b*(lambda[1]+I*lambda[2])+a)+b*x)+y*((lambda[1]+I*lambda[2])*y+x))+b*t^2-t*y)+4*(-2*((I*lambda[1]*lambda[2]+(1/2)*lambda[1]^2-(1/2)*lambda[2]^2)*b+a*(lambda[1]+I*lambda[2]))*x*y-(lambda[1]+I*lambda[2])*x^2*b-2*a*x^2+12*alpha)*beta^2+2*beta*(-4*a*(b*(lambda[1]+I*lambda[2])+a)*t^2+t*(y*(b*(lambda[1]^2-lambda[2]^2+(2*I)*lambda[1]*lambda[2])+2*a*(lambda[1]+I*lambda[2]))+2*(b*(lambda[1]+I*lambda[2])+2*a)*x)+x*((lambda[1]+I*lambda[2])*y+x))+((b*(lambda[1]+I*lambda[2])+2*a)*t-(lambda[1]+I*lambda[2])*y-2*x)*t)

 (2)
> 

ans := solve({diff(rhs(equ), x), diff(rhs(equ), y)}, {x, y}, explicit)
 

``

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