Question

the complete integral of z=px+qy+pq is​

Answer 1

Answer:

z=px+qy+pq, where

p=az/ax,q= az/at

the given equation

f (x, y, 2, p, q) = px + py + pq-z.

ds= dp/0 = dq/0 = dz/z+pq=dx/ x+q

=dy/y+p

now , from

ds=dp/0, ds = dq/0= p= c,q= D

bring arbitary constants .now I have to use

dz= pdx+ qdy= cdx+ 0dy

we get

z (x,y)= cx+ Dy + E.

Answer 2

The complete integral of z = px + qy + pq is z = ax + by + ab

Given :

The equation z = px + qy + pq

To find :

The complete integral of z = px + qy + pq

Concept :

Equation of the form z = px + qy + f (p,q) is known as Clairaut's Equation

The complete integral is given by

z = ax + by + f (a,b)

Where a and b are constants

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

z = px + qy + pq

The above equation is of the form

z = px + qy + f (p,q)

Which is known as Clairaut's Equation

Step 2 of 2 :

Find the complete integral

We know that complete integral of z = px + qy + f (p,q) is given by

z = ax + by + f (a,b)

Hence for the given equation z = px + qy + pq the complete integral is z = ax + by + ab

Where a and b are constants

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ M+N(dy/dx)=0 where M and N are function of

https://brainly.in/question/38173299

2. This type of equation is of the form dy/dx=f1(x,y)/f2(x,y)

https://brainly.in/question/38173619