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


Failed

Maple


\[\left \{u \left (x , y\right ) = x y +c_{1}-i \mathit {\_F1} \left (-i x +y \right )+i \mathit {\_F2} \left (i x +y \right ), v \left (x , y\right ) = \frac {x^{2}}{2}+\mathit {\_F1} \left (-i x +y \right )+\mathit {\_F2} \left (i x +y \right )\right \}\]