2.12.2 Cauchy Riemann PDE With extra term on right side

problem number 107

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'));
 

\[\left \{u \left (x , y\right ) = -i f_{1} \left (-i x +y \right )+i f_{2} \left (i x +y \right )+y x +c_{1}, v \left (x , y\right ) = f_{1} \left (-i x +y \right )+f_{2} \left (i x +y \right )+\frac {x^{2}}{2}\right \}\]