  We consider a bi-layer consisting of a $d-$wave layerd superconductor and
diffusive ferromagnet with a domain wall (DW). The $c-$axis in the
superconductor and DW in the ferromagnet are assumed to be perpendicular to the
interface. We demonstrate that in such a heterostructure the inhomogeneous
exchange field enhances the proximity effect. It is shown that, whereas in the
absence of the exchange field the $d-$wave condensate decays in the normal
metal on the mean free path $l$, the superconductivity penetrates the
ferromagnet along the DW over much larger distances. This happens because the
presence of DW results in a generation of an odd frequency triplet s-wave
component of the condensate. The phenomenon discovered here may help to explain
a recent experiment on high temperature superconductor-ferromagnet bi-lyers.

Superconductivity;Mesoscale and Nanoscale Physics