#### 7.48 Bug in dsolve in Maple V.4 to Maple 6 (19.2.97)

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)