Question

1: Solve by PDEs
(y-z)p+(z-x)q=x-y​

Answer 1

Answer:

This is Lagrange's linear equation Pp+Qq=RPp+Qq=R

∴∴ The auxiliary equation is

dxy−z=dyz−x=dzx−ydxy−z=dyz−x=dzx−y

Each is equal to dx+dy+dzy−z+z−x+x−ydx+dy+dzy−z+z−x+x−y

=d(x+y+z)0=d(x+y+z)0

⇒d(x+y+z)=0⇒d(x+y+z)=0

∴∴ On Integration, x+y+z=ax+y+z=a

Also, each ratio is equal to

xdx+ydy+zdzx(y−z)+y(z−y5)+z(x−y)xdx+ydy+zdzx(y−z)+y(z−y)+z(x−y)

=12d(x2+y2+z2)

PLEASE MARK AS BRAINLIEST