I’ve just discovered a bug that Release 4 seems to have introduced to dsolve. As an example to my students I offered the following homogeneous equation
> de:= diff(y(x),x)= y(x)/x + tan(y(x)/x); > cond:=y(1)=Pi/3;
dsolve in Release V.3 gave the answer
> y(x) = x*arcsin(x*sqrt(3)/2)
but in V.4 two (!!) solutions are returned, one of which is the previous - in the less friendly form
y(x) = x*arctan(x/sqrt(4/3 - x^2))
The other solution is the negative of this (and so is wrong as it does not satisfy the condition at x=1).
If one of the solutions is extracted for examination, it changes form yet again to
x*arctan(x*sqrt(-9x^2 - 12)/(3*x^2 - 4))
[I know this bug all has to do with branches in the complex plane, but my students have no idea about that.]
It is corrected with Maple 7. (U. Klein)