Mathquery

Non_ Linear Partial Differential Equation Of First Order :          Let us consider a differential equation of the form F(x,y,p,q) = 0 in which the function F is not necessarily linear in p and q .   Singular solution / Singular Integral :               The equation of the envelop of the surface represented by the complete integral of a partial differential equation is called its singular solution or singular integral .       The envelop of the surface F(x,y,a,b)=0  is obtained by eliminating a and b from the equations F = 0 , ∂F/∂a = 0,  ∂F/∂b = 0  Charpit's Method :          Let us consider the equation f(x,y,p,q) = 0 then Charpit's subsidiary equations are given by   dx/ [∂f/∂p] = dy/ [∂f/∂q]                      = dz/[p(∂f/∂p) + q(∂f/∂q)]     ...