In this case Maple yields directly
1
y(x) = -----------
1 + exp(-x)
In case it gave directly the answer in terms of ln(y), option 'explicit'
might generate the solution above. Is there no equivalent in Maxima?
J. F. Ogilvie
On Tue, 28 May 2013, David Billinghurst wrote:
> On 28/05/2013 1:52 PM, 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).
>>
>> 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
>>
>
> Not easily :-(. I couldn't find a good, general solution when I wrote
> contrib_ode, so I gave up.