DSolve[{y*(D[su[x,y],{x,2}]-D[su[x,y],{y,2}])-2x*D[su[x,y],x,y]-D[su[x,y],y]==0,su["0",y]==1/Cosh[y],D[su[x,y],x]==0/.x->"0"},su,{x,y}]
Out[]=
DSolve-[x,y]-2x[x,y]+y-[x,y]+[x,y]0,su[0,y]Sech[y],[0,y]0,su,{x,y}
(0,1)
su
(1,1)
su
(0,2)
su
(2,0)
su
(1,0)
su