Partial Differential Equations

2 First-Order Partial Differential Equations

A differential equation involving first-order partial derivatives of the dependent variables with respect to independent variables is called a partial differential equation of the first order. The equation can be written in the form, $\varphi \left(x_1,x_2,\mathrm{..}.x_n,u_{x_1},u_{x_2},\mathrm{..}.u_{x_n}\right)=0$. In this chapter, we shall study two main concepts of partial differential equations namely first-order linear partial differential equations and first-order non-linear partial differential equations. In the section on linear first-order partial differential equations, we shall learn the solution procedure of Lagrange’s equation of the first order with a sufficient number of examples. In the section on non-linear first-order partial differential ...