Given z = ( x 2 +a 2 ) ( y 2 + b 2) …….(1)ĭifferentiating (1) partially w.r.t x & y, we get Which is the required partial differential equation.įorm the partial differential equation by eliminating the arbitrary constants a and b from Partial differential equations can be obtained by the elimination of arbitrary constants or by the elimination of arbitrary functions.īy the elimination of arbitrary constantsį ( x, y, z, a, b ) = 0 - (1)ĭifferentiating equation (1) partially w.r.t x & y, we getĮliminating a and b from equations (1), (2) and (3), we get a partial differential equation of the first order of the form f (x,y,z, p, q) = 0Įliminate the arbitrary constants a & b from z = ax + by + abĬonsider z = ax + by + ab _ (1)ĭifferentiating (1) partially w.r.t x & y, we get
If each term of such an equation contains either the dependent variable or one of its derivatives, the equation is said to be homogeneous, otherwise it is non homogeneous.Ģ Formation of Partial Differential Equations We shall denoteĪ partial differential equation is linear if it is of the first degree in the dependent variable and its partial derivatives. But, here we shall consider partial differential only equation two independent variables x and y so that z = f(x,y). A partial differential equation contains more than one independent variable. The order of the highest derivative is called the order of the equation. This unit covers topics that explain the formation of partial differential equations and the solutions of special types of partial differential equations.Ģ FORMATION OF PARTIAL DIFFERNTIAL EQUATIONSģ SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONSĥ PARTIAL DIFFERENTIAL EQUATIONS OF HIGHER ORDER WITH CONSTANT CO-EFFECIENTSĪ partial differential equation is one which involves one or more partial derivatives.