I'm having trouble with solving this system of ODE's using Maple software:
$\frac{2q(3q-1)}{\tau^2}f_{1,R}+2\frac{q}{\tau}\dot{f}_{1,R}+\ddot{f}_{1,R}+(\kappa^2+f_{2,T})(1+\omega)(\tau/\tau_0)^{(-3(3+\omega)q)}=0$
and $\frac{(-30q^2+54q^3+4q)}{\tau^3}f_{1,R}+\frac{(-4q+24q^2)}{\tau^2}\dot{f}_{1,R}+\frac{11q}{\tau}\ddot{f}_{1,R}+\dddot{f}_{1,R}-3\omega(1+\omega)(\kappa^2+f_{2,T})\frac{q}{\tau}(\tau/\tau_0)^{-3(1+\omega)q}=0 $
They're equations from this paper https://arxiv.org/abs/1710.01910 (45 and 47) With functions $f_{1,R}(\tau)$ and $f_{2,R}(\tau)$, ($\dot{f}=df/d\tau$) and where $q,\omega,\kappa,\tau_0$ are constants.
Solutions should be:
$f_{1,R}(\tau)=C_+\tau^{\mu_+}+C_-\tau^{\mu_=}+A\tau^{-9q+2}$
$f_{2,T}(\tau)=-A(\frac{69q^2-25q+2}{1+\omega})\tau_0^{-9q}(\tau/\tau_0)^{3\omega q}-\kappa^2$
where $C$'s and $A$ are integration constants and $\mu{\pm}=\frac{-2q+1\pm\sqrt{-20q^2+4q+1}}{2}$;
Here, i listed my maple code ($\tau=t,\;\omega=w,\;f_{1,R}=f1(t)\;,f_{2,T}=f2(t)$:
sysode := 2*q*(3*q-1)*f1(t)/t^2+2*q*(diff(f1(t), t))/t+diff(f1(t), t, t)+(kappa^2+f2(t))(1+w)(t/t0)^(-(3*(3+w))*q) = 0, (54*q^3-30*q^2+4*q)*f1(t)/t^3+(24*q^2-4*q)*(diff(f1(t), t))/t^2+11*q*(diff(f1(t), t, t))/t+diff(f1(t), t, t, t)-3*w*(1+w)*(kappa^2+f2(t))q(t/t0)^(-(3*(1+w))*q)/t = 0;
simplify(dsolve([sysode], build))
However, my solutions are much more complicated than those listed above: https://i.stack.imgur.com/uJj0e.png
So, there is my question. How to get rid of hypergeom functions in these solutions ? (I have noticed that function $f1(t)=f_{1,r}(\tau)$ wouldve been correct when no hypergeom factor is present)