Solution: Given that, Let, f(x, y, z, p, q) = p – 3x^2 – q^2 –y Now, fx = – 6x fy= 1 fz= 0 fp=1 fq= – 2q We know that the charpitals auxiliary system is Taking 1st and 4th ratio, we get ⇒dp=6xdx Integrating we get, p = ...

Read More »## Complete Solution of Charpit’s method

Solution: Consider the non-linear partial differential equation f(x, y, z, p, q)= 0 —————————-(1) Since z is a function of x and y, it follows that dz = pdx + qdy —————————————–(2) Let us assume p=u (x, y, z, a), where a is arbitrary constant, substitute in (1) solve to ...

Read More »## Partial differential equation

Definition: An equation involving partial derivatives is called partial differential equation. Shortly it is written as P.D.E. Some notation for derivatives: Formulation of partial differential equation: (i) Elimination of arbitrary constant and (ii) Elimination of arbitrary function. Procedure of elimination of arbitrary constant: Let us consider the relation g(x,y,z,a,b)=0 ———————————-(i) ...

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