I have two coupled differential equations as follows \begin{eqnarray} \frac{\partial }{\partial x}U[x,y] &=&2V[x,y], \notag \\ \frac{\partial }{\partial y}V[x,y] &=&V[x,y]U[x,y]+1, \end{eqnarray} with conditions \begin{equation} U[0,y]=\sin [y]\,,\qquad V[x,0]=0. \end{equation} To solve the above equations with the NDSolve command in Mathematica, the following errors are obtained
Can you help me fix this?