On 05/28/2013 04:52 AM, Alasdair McAndrew wrote:
> If I want to solve the ivp
>
> y' = y(1-y), y(0)=1/2
>
> (a logistic equation), I can use either
>
> ic1(ode2('diff(y,x)=y*(1-y),y,x),x=0,y=1/2);
>
> or
>
> ic1(contrib_ode('diff(y,x)=y*(1-y),y,x),x=0,y=1/2);
>
> both of which give me as a solution
>
> log(y)-log(y-1) = x - log(2) - log(-1/2)
>
> instead of
>
> y = exp(x)/(exp(x)+1).
(%i2) load("to_poly_solver");
(%i3) ic1(ode2('diff(y,x)=y*(1-y),y,x),x=0,y=1/2);
(%o3) log(y)-log(y-1) = x-log(2)-log(-1/2)
(%i4) %solve(%,y);
(%o4) %union([y = %e^x/(%e^x+1)])
Jaime