Hello, I have been trying to solve the system below but it executes forever and doesn't seem to find an answer.
F[x_]:=x/(1+x)
lambda=l1+l2+l3
c1=RandomReal[3]
c2=RandomReal[3]
c3=RandomReal[3]
c4=RandomReal[3]
pn=(P1^(-2)+P2^(-2)+P3^(-2)+(P4*F[lambda]/2)^(-2))^(-1/2)
s1=(P1/pn)^(-1/2)
s2=(P2/pn)^(-1/2)
s3=(P3/pn)^(-1/2)
s4=(P4/pn)^(-1/2)
Solve[P1\[Equal] (2*(1-s1))/(3*(1-s1)+s1)*c1&&P2\[Equal] (2*(1-s2))/(3*(1-s2)+s2)*c2&&P3==(2*(1-s3))/(3*(1-s3)+s3)*c3&& P4\[Equal] (2*(1-s4))/(3*(1-s4)+s4)*c4&&y*(1-c1/P1)*2*s1*(s4)\[Equal](1+F[lambda]/2)^3 /(D[F[lambda],l1]/2)&&y*(1-c2/P2)*2*s2*(s4)\[Equal](1+F[lambda]/2)^3 /(D[F[lambda],l2]/2)&&y*(1-c3/P3)*2*s3*(s4)\[Equal](1+F[lambda]/2)^3 /(D[F[lambda],l3]/2),{P1,P2,P3,P4,l1,l2,l3}]
I have been trying to solve the equations one after the other in the following way :
sol1=Solve[P1 == (2*(1-s1))/(3*(1-s1)+s1)*c1,{P1}]
X1=Array[x1,{Length@sol1}]
x1[k_] /; MemberQ[Range[Length@sol1],l] :=sol1[[k,1,2]]
P1=X1
sol2=Solve[P2 == (2*(1-s2))/(3*(1-s2)+s2)*c2,{P2}]
X2=Array[x2,{Length@sol2}]
x2[k_] /; MemberQ[Range[Length@sol2],l] :=sol2[[k,1,2]]
P2=X2
The first part works and I was planning to continue this way but the second part returns with a serie of errors. And still, even the first part takes a very long time to run...
Can you tell please tell me why it doesn't work or/and whether there is an other way to have a result in a faster way?
