Question

the complete integrel of z=px+qy+√1+p²+q² is​

Answer 1

The complete integral of z = px + qy + √(1 + p² + q²) is z = ax + by + √(1 + a² + b²) Where a and b are constants

Given :

The equation z = px + qy + √(1 + p² + q²)

To find :

The complete integral of z = px + qy + √(1 + p² + q²)

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 + √(1 + p² + q²)

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 + √(1 + p² + q²) the complete integral is z = ax + by + √(1 + a² + b²)

Where a and b are constants

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