Question: ODE System Solve

c10:=-26/9:c01:=-9.330480048:c11:=-199/33:c02:=-7.162134941:c12:=-93/11:c03:=-.756797589:d10:=11/9:d01:=26/9:d11:=19/3:d02:=25/3:d12:=8:d03:=1:

aa1:=diff(arctan(v/u),u):bb1:=diff(arctan(v/u),v):

w :=-c01*d10+c10*d01:

f11 := subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, -A1): collect(%, v):f2 := subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, B1): collect(%, v):g := simplify(-c10*f11/sqrt(w)+c01*f2/sqrt(w)): collect(%, v):

f111:=collect(1/sqrt(w)*f11,v):f222:=collect(1/sqrt(w)*g,v):

F1:=u*f111+v*f222:F11:=subs({u=r*cos(theta),v=r*sin(theta)},F1):F11:=F11/r:F2:=aa1*f111+bb1*f222:F22:=subs({u=r*cos(theta),v=r*sin(theta)},F2):

M:=F11/F22:M:=taylor(M,r,6):r1:=coeff(M,r,1):simplify(%):subs(c10=-d01,r1):simplify(%):

c10:=-d01:R2:=coeff(M,r,2):R3:=coeff(M,r,3):R4:=coeff(M,r,4):R5:=coeff(M,r,5):

#R2,R3,R4,R5 have been given,I try to solve the following ode equation: The initial value:r2(0)=r3(0)=r4(0)=r5#(0);system={diff(r2(theta),theta)=R2;diff(r3(theta),theta)=2*R2*U2+R3;diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4;diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5}.I want to get the exact solution of subs(theta=2*Pi,U5),But it just gives the form include _Z1,_Z_2,_Z3.How can I get exact value?

U2:=rhs(dsolve({diff(r2(theta),theta)=R2,r2(0)=0})):

U3:=rhs(dsolve({diff(r3(theta),theta)=2*R2*U2+R3,r3(0)=0})):

U4:=rhs(dsolve({diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4,r4(0)=0})):

U5:=rhs(dsolve({diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5,r5(0)=0})):

U6:=subs(theta=2*Pi,U5):save U6, output5: