Question

(x2 - y2 - z2)p + 2xyq = 2xz​

Answer 1

Answer:

Explanation:

hope it helps

Answer 2

The given equation is in Lagrange's linear equation

                      Pp + Qq = R

The equation will be,

                dx/x²- y²-z² = dy/2xy = dz/2xz..[1]

                          using the last two ratios,    dy/2xy = dz/2xz

                                                                     ⇒ dy/y = dz/z

Integrating log y = log z + log a

              ⇒ y/z = a

Taking x, y, z from[1]

          = xdx+ ydy+ zdz/x(x²+ y²+ z²)

   now,

              dy/2xy = xdx+ ydy+ zdz/x(x²+ y²+ z²)

                  dy/y = d(x²+ y²+ z²)/x²+ y²+ z²

Integrating,

               log y = log( x²+ y²+ z²)+ log b

                    y/x²+ y²+z² = b

         ∴ the general equation is ∅ (y/z, y/x²+ y²+z²) = 0.