In[]:=
$Version
Out[]=
14.2.0 for Microsoft Windows (64-bit) (December 26, 2024)
In[]:=
DSolve[{y*(D[U[x,y],{x,2}]-D[U[x,y],{y,2}])-2x*D[U[x,y],x,y]-D[U[x,y],y]==0,U[0,y]==1/Cosh[y],Derivative[1,0][U][0,y]==0},U[x,y],{x,y}]​​
Out[]=
DSolve[{-
(0,1)
U
[x,y]-2x
(1,1)
U
[x,y]+y(-
(0,2)
U
[x,y]+
(2,0)
U
[x,y])0,U[0,y]Sech[y],
(1,0)
U
[0,y]0},U[x,y],{x,y}]
In[]:=
DSolve[{y*(D[U[x,y],{x,2}]-D[U[x,y],{y,2}])-2x*D[U[x,y],x,y]-D[U[x,y],y]==0},U[x,y],{x,y}]
Out[]=
DSolve[{-
(0,1)
U
[x,y]-2x
(1,1)
U
[x,y]+y(-
(0,2)
U
[x,y]+
(2,0)
U
[x,y])0},U[x,y],{x,y}]
Maple 2025 solution: