Question: Strange dsolve bug for a simple ODE

(Maple 2015)

For the simple ODE with initial condition
dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3, y(0) = 1/10 }, y(t));

dsolve produces two different answers, almost randomly (even after restart or after closing Maple and reloading the worksheet). Namely:

(1)

(2)

or

(2')

but this simplifies to (2), so it's not a "true" bug.

Notice that (2) is correct but (1) is incorrect even for t=0 (the initial condition!):

evalf(eval(RootOf(-ln(_Z)*_Z+ln(_Z-1)*_Z-ln(10)*_Z-ln(9/10)*_Z-I*Pi*_Z+_Z*t-10*_Z+1),t=0))=1/10;

Maple seems to prefer the wrong solution (1) but occasionally produces (2) e.g. in a new whorksheet!
In earlier versions it seems that only (1)  appears.

The same ODE with another IC

dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3, y(0) = 1/100 }, y(t));

 

evalf(eval(%,t=0));

 

is always incorrect. It should be

 

but Lambert's function never shows up!
Let me mention that only the exact solutions are affected, numeric is ok.

Without an initial condition, dsolve always uses LambertW:

dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3}, y(t));

 

 

Can you explain this behavior?

 

 

Please Wait...