Systems of partial diff. equations of the first order

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Problem: Find the general solution of the system of linear partial differential equations of the first order: \[ \left\{\begin{array}{l} \frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}=0 \\ \frac{\partial u}{\partial y}-\frac{\partial v}{\partial x}=0 \end{array}\right. \]

11.6.4 Systems of equations in partial derivatives of the first order

5.08 $

Problem: Determine the type of the system of linear partial differential equations of the first order: \[ \left\{\begin{array}{l} u_{x}+v_{x}-u_{y}+v_{y}=x y \\ 2 v_{y}-v_{x}+u_{x}+3 u_{y}=u \end{array}\right. \]

11.6.1 Systems of equations in partial derivatives of the first order

2.54 $

Problem: Determine the type of the system of linear partial differential equations of the first order: \[ \left\{\begin{array}{l} u_{y}+3 v_{x}-v_{y}=y \\ 2 v_{y}-v_{x}=x \end{array}\right. \]

11.6.2 Systems of equations in partial derivatives of the first order

2.54 $

Problem: Determine the type of the system of linear partial differential equations of the first order: \[ \left\{\begin{array}{l} 3 u_{x}+4 u_{y}-v_{y}+v_{x}=0 \\ u_{x}+v_{y}-v_{x}=0 \end{array}\right. \]

11.6.3 Systems of equations in partial derivatives of the first order

0 $