Is there something other than ode2 that attempts to
solve a first order DE that is nonlinear in the
derivative? Something like
(%o65) ('diff(r,t,1))^2=(2*r^2+2*r-1)/r^2
(%i66) ode2(%,r,t);
(%t66) ('diff(r,t,1))^2=(2*r^2+2*r-1)/r^2
first order equation not linear in y'
(%o66) false
OK solve for the derivative and use ode2:
(%i67) solve(%o65,diff(r,t));
(%o67)
['diff(r,t,1)=-sqrt(2*r^2+2*r-1)/r,'diff(r,t,1)=sqrt(2*r^2+2*r-1)/r]
(%i68) ode2(second(%),r,t);
(%o68)
(sqrt(2)*sqrt(2*r^2+2*r-1)-log(2*sqrt(2)*sqrt(2*r^2+2*r-1)+4*r+2))/(2*sqrt(2))=t+%c
Barton