2.12.2 Cauchy Riemann PDE With extra term on right side

problem number 108

Solve for \(u(x,y),v(x,y\) \begin {align*} \frac {\partial u}{\partial x} &= \frac {\partial v}{\partial y}\\ \frac {\partial u}{\partial y} &= -\frac {\partial v}{\partial x} + y \end {align*}

Mathematica ✗

ClearAll["Global`*"]; 
ClearAll[u, v, x, y]; 
 pde1 = D[u[x, y], x] == D[v[x, y], y]; 
 pde2 = D[u[x, y], y] == -D[v[x, y], x] + y; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[{pde1, pde2}, {u[x, y], v[x, y]}, {x, y}], 60*10]];
 

Failed

Maple ✓

restart; 
pde1:= diff(u(x,y),y)=diff(v(x,y),x); 
pde2:= diff(u(x,y),x)=-diff(v(x,y),y)+y; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde1,pde2],[u(x,y),v(x,y)])),output='realtime'));
 

\[ \left \{ u \left ( x,y \right ) =-i{\it \_F1} \left ( y-ix \right ) +i{\it \_F2} \left ( ix+y \right ) +yx+{\it \_C1},v \left ( x,y \right ) ={\it \_F1} \left ( y-ix \right ) +{\it \_F2} \left ( ix+y \right ) +1/2\,{x}^{2} \right \} \]