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# Solve a nonlinear system of equation via sympy

I have a system of ODE and want to find equilibrium points by using nonlinsolve() but when i run it by jubyter or spyder the program keep running without any result.

``````N,x1,x2,x3,x4,y1,y2,r1,r2,r3,r4,eta1,eta2,eta3,eta4,R,c1,c2,c3,c4,a11,a12,a21,a22,a31,a32,a41,a42,b12,h,h11,h12,h21,h22,h31,h32,h41,h42,s1,s2,s3,s4,epsilon1,epsilon2,omega1,omega2,K11,K22,beta11,beta21,beta31,beta41,beta12,beta22,beta32,beta42,gamma12=sp.symbols('x1,x2,x3,x4,y1,y2,r1,r2,r3,r4,eta1,eta2,eta3,eta4,N,R,c1,c2,c3,c4,a11,a12,a21,a22,a31,a32,a41,a42,b12,h,h11,h12,h21,h22,h31,h32,h41,h42,s1,s2,s3,s4,epsilon1,epsilon2,omega1,omega2,K11,K22,beta11,beta21,beta3a,beta41,beta12,beta22,beta32,beta42,gamma12')

F1=R-c1*x1-c2*x2-c3*x3-c4*x4

F2=x1*(r1*(1-(eta1*x1+eta2*x2+eta3*x3+eta4*x4)/N)-(a11*y1)/(y1+a11*h11*x1)-(a12*y2)/(y2+a12*h12*x1))+s1

F3=x2*(r2*(1-(eta1*x1+eta2*x2+eta3*x3+eta4*x4)/N)-(a21*y1)/(y1+a21*h21*x2)-(a22*y2)/(y2+a22*h22*x2))+s2

F4=x3*(r3*(1-(eta1*x1+eta2*x2+eta3*x3+eta4*x4)/N)-(a31*y1)/(y1+a31*h31*x3)-(a32*y2)/(y2+a32*h32*x3))+s3

F5=x4*(r4*(1-(eta1*x1+eta2*x2+eta3*x3+eta4*x4)/N)-(a41*y1)/(y1+a42*h41*x4)-(a42*y2)/(y2+a42*h42*x4))+s4

F6=y1*(-epsilon1*(1+(y1+omega2*y2)/K22)-(b12*y2)/(y2+b12*h*y1)\
+beta11*(a11*x1)/(y1+a11*h11*x1)\
+beta21*(a21*x2)/(y1+a21*h21*x2)\
+beta31*(a31*x3)/(y1+a31*h31*x3)\
+beta41*(a41*x4)/(y1+a41*h41*x4))

F7=y2*(-epsilon2*(1+(omega1*y1+y2)/K11)-gamma12*(b12*y1)/(y2+b12*h*y1)\
+beta12*(a12*x1)/(y2+a12*h12*x1)\
+beta22*(a22*x2)/(y2+a22*h22*x2)\
+beta32*(a32*x3)/(y2+a32*h32*x3)\
+beta42*(a42*x4)/(y2+a42*h42*x4))
equ=(F1,F2,F3,F4,F5,F6,F7)
sol=nonlinsolve(equ,N,x1,x2,x3,x4,y1,y2)

``````

Is it possible to get the solution in terms of parameters?