From: david.billinghurst (Billinghurst, David RTATECH)
Date: Tue, 5 Dec 2006 09:38:02 +1100
> From: Barton Willis
>
> 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
contrib_ode returns a parametric solution in terms of dummy variable %t.
Not sure if is correct. I didn't try to clean it up.
See share/contrib/diffequations/tests for a few hundred examples.
(%i1) eqn:('diff(r,t,1))^2=(2*r^2+2*r-1)/r^2;
2
dr 2 2 r + 2 r - 1
(%o1) (--) = --------------
dt 2
r
(%i2)
load('contrib_ode);
(%o2)
/usr/local/share/maxima/5.10.0/share/contrib/diffequations/contrib_ode.mac
(%i3) contrib_ode(eqn,r,t);
2
dr 2 2 r + 2 r - 1
(%t3) (--) = --------------
dt 2
r
first order equation not linear in y'
2 3/2
log(3 - %t ) 2 %t - 2
------------ log(-----------)
/ 2 2 3/2
[ (%t - 4) %e 2 %t + 2 %t
(%o3) [[t = I ------------------------- d%t + ---------------- + ---------
] 6 4 2 4 sqrt(2) 2
/ %t - 7 %t + 16 %t - 12 2 %t - 4
2
log(3 - %t )
------------
2 / 2 2
sqrt(3 - %t ) - 1 [ (%t - 4) %e
+ %c, r = - -----------------], [t = - I ------------------------- d%t
2 ] 6 4 2
%t - 2 / %t - 7 %t + 16 %t - 12
3/2
2 %t - 2
log(-----------)
3/2 2
2 %t + 2 %t sqrt(3 - %t ) + 1
+ ---------------- + --------- + %c, r = -----------------]]
4 sqrt(2) 2 2
2 %t - 4 %t - 2
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