Exact Solutions > Nonlinear Partial Differential Equations > Other Second-Order Partial Differential Equations ## 4. Other Second-Order Partial Differential Equations## 4.1. Equations of Transonic Gas Flow-
*a**w*_{x}*w*_{xx}+*w*_{yy}= 0. Equation of steady transonic gas flow. -
*w*_{yy}+*a**y*^{−1}*w*_{y}+*b**w*_{x}*w*_{xx}= 0. Equation of steady transonic gas flow.
## 4.2. Monge-Ampere Equations-
(
*w*_{xy})^{2}−*w*_{xx}*w*_{yy}= 0. Homogeneous Monge-Ampere equation. -
(
*w*_{xy})^{2}−*w*_{xx}*w*_{yy}=*A*. Nonhomogeneous Monge-Ampere equation. -
(
*w*_{xy})^{2}−*w*_{xx}*w*_{yy}=*F*(*x*,*y*). Nonhomogeneous Monge-Ampere equation.
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