I asked this question about the analytical solution of the PDE :

$ $ \partial_t c=\partial_x((c-a)(c-b)\partial_xc) $ $

And I was given the answer that Maple gives the following implicit form as a solution :

$ $ \eqalign{&{k_{{1}}}^{2}{k_{{2}}}^{2}{c}^{2} + \left( 2\,{k_{{1}}}^{4}k_{{2}}k_{{3

}}-2\,{k_{{1}}}^{2}{k_{{2}}}^{2}a-2\,{k_{{1}}}^{2}{k_{{2}}}^{2}b

\right) c\cr &+ \left( 2\,{k_{{1}}}^{6}{k_{{3}}}^{2}-2\,a{k_{{1}}}^{4}k_{{

2}}k_{{3}}-2\,b{k_{{1}}}^{4}k_{{2}}k_{{3}}+2\,ab{k_{{1}}}^{2}{k_{{2}}}

^{2} \right) \ln \left( -{k_{{1}}}^{2}k_{{3}}+ck_{{2}} \right)\cr & -2\,{k

_{{2}}}^{4}t-2\,k_{{1}}{k_{{2}}}^{3}x-2\,{k_{{2}}}^{3}k_{{3}}-2\,k_{{4

}}{k_{{2}}}^{3}

=0}

$ $

But when I’m doing the $ DSolve$ on Mathematica (I don’t have Maple) I get no solution !

So my question is : can Mathematica give me that implicit solution ? Can Maple do things that Mathematica cannot ?