Non_ Linear Partial Differential Equation Of First Order
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)] = dp/-(∂f/∂x + p∂f/∂z) = dq / -(∂f/∂y + q∂f/∂z) Application Of Charpit's Method : Example : Find the com