Question

((y-z)p+(z-x)q)=x-y solve​

Answer 1

Answer:

Correct Answer:

A) ϕ(x+y+z,x2+y2+z2)=0

Description for Correct answer:

(y−z)p+(z−x)q=x−y

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

∴ The auxiliary equation is

dx

y−z

=

dy

z−x

=

dz

x−y

Each is equal to

dx+dy+dz

y−z+z−x+x−y

=

d(x+y+z)

0

⇒d(x+y+z)=0

∴ On Integration, x+y+z=a

Also, each ratio is equal to

xdx+ydy+zdz

x(y−z)+y(z−y)+z(x−y)

=

1

2

d(x2+y2+z2)

0

⇒d(x2+y2+z2)=0

Integrating, x2+y2+z2=b

∴ The general solution is

ϕ(x+y+z,x2+y2+z2)=0

Step-by-step explanation:

Hope this will help you