Question

Solve the pde z=px+qy+p^2+q^2+pq solution

Answer 1

Answer:

if the equation is of the form z = px + qy + f(p,q)

then the solution is z = ax + by + f(a,b)

Answer 2

The solution of the PDE z = px + qy + p² + q² + pq is z = ax + by + a² + b² + ab

Given :

The equation z = px + qy + p² + q² + 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 + p² + q² + 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 PDE z = px + qy + p² + q² + pq the solution is given by is z = ax + by + a² + b² + ab

Where a and b are constants

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