Differential equations?



Alasdair McAndrew <amca01 <at> gmail.com> writes:

> 
> 
> 
> 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).
> 
> I can obtain this solution by some fiddling with
 Maxima's output, but is there any way of 
obtaining the "correct" solution directly?
> 
> Thanks,Alasdair
> 
> 
> 
> 
> -- Blog: http://amca01.wordpress.comWeb:? http://sites.google.com/site/amca01/
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> 
>

 
> 
> 
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Here is what I did:

deq:'diff(y,x)=y*(1-y);
sol:ode2(deq, y, x);
sol:ic1(sol, x=0, y=1/2);
logcontract(sol);
solve(%, y);

- Michael