Question

Eliminate Φ from the equation and form Partial Differential equation. Φ(x²-y², xy-z)=0​

Answer 1

Step-by-step explanation:

The function F( x^2+ y^2 , Z - xy ) = 0 , with Z =Z(x,y) can be written as

F ( u , v ) =0 , with u = x^2 + y^2 , v = Z - xy . Differentiating respect to x and y

F_x = (F_u)2x + (F_v)( Z_x - y ) =0

F_y = (F_u)2y + (F_v)( Z_y - x ) =0 .Elimination of F_u and F_v gives

2x( Z_y - x ) -2y( Z_x - y ) =0 . Then the DE is

xZ_y - yZ_x = x^2 - y^2 .