On Aug 20, 2009, at 4:20 PM, Vinzent Steinberg wrote:
> Interesting behavior (not very creative, but hey, I'm an ODE noob): > > >>> dsolve(f-f.diff(x, 1), f) > f(x) == exp(C1 + x) > >>> dsolve(f-f.diff(x, 2), f) > f(x) == C1*exp(x) + C2*exp(-x) > >>> dsolve(f-f.diff(x, 3), f) > f(x) == C1*exp(x) + (C2*sin(x*3**(1/2)/2) + C3*cos(x*3**(1/2)/ > 2))*exp(-x/2) > >>> dsolve(f-f.diff(x, 5), f) > f(x) == C1*exp(-x/4 + x*5**(1/2)/4)*sin(x*(5/8 + 5**(1/2)/8)**(1/2)) > + C2*exp(-x/4 + x*5**(1/2)/4)*sin(x*(5/8 + 5**(1/2)/8)**(1/2)) + > C3*exp(-x/4 - x*5**(1/2)/4)*sin(x*(5/8 - 5**(1/2)/8)**(1/2)) + > C4*exp(-x/4 - x*5**(1/2)/4)*sin(x*(5/8 - 5**(1/2)/8)**(1/2)) + > C5*exp(x) + C6*cos(x*(5/8 + 5**(1/2)/8)**(1/2))*exp(-x/4 + > x*5**(1/2)/4) + C7*cos(x*(5/8 + 5**(1/2)/8)**(1/2))*exp(-x/4 + > x*5**(1/2)/4) + C8*cos(x*(5/8 - 5**(1/2)/8)**(1/2))*exp(-x/4 - > x*5**(1/2)/4) + C9*cos(x*(5/8 - 5**(1/2)/8)**(1/2))*exp(-x/4 - > x*5**(1/2)/4) When you have an ode of the form a_n*f^(n) + a_n-1*f^(n-1) + ... a_1*f' + a_0*f = 0, where a_i is constant for all i, the solution is based on the roots of the characteristic equation a_n*m**n + a_n-1*m**(n-1) + ... + a_1*m + a_0 = 0. So you are getting that crazy result because of the result of solve(-x**5 + 1, x), as well as doing re() and im() on the roots. > Don't know whether it makes sense to add this trivial special case. I don't see how that is a special case, but I don't like adding special cases anyway. I think that every ode that you want it to solve should be done with a general method. That way the code is cleaner and more robust. For example, we used to have a special case code (see ODE_1 in the current master), but I replaced it with the Liouville ODE method, and now it can do more and is much cleaner. > The other ODEs I "invented" were mostly not solvable. :( > > Do you think solve should recognize ODEs? > > >>> dsolve(f-f.diff(x), f) > f(x) == exp(C1 + x) > >>> solve(f-f.diff(x), f) > [0] > solve() should stick to algebraic solving, because sometimes you want to actually solve for f. I wonder though if it should return f.diff(x) in that second one. Every CAS that I know of has a separate solver for algebraic solving and differential equation solving. Aaron Meurer > Vinzent > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy-patches" group. To post to this group, send email to sympy-patches@googlegroups.com To unsubscribe from this group, send email to sympy-patches+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sympy-patches?hl=en -~----------~----~----~----~------~----~------~--~---
