Question

z = ax + a^2 y^2 + b form the pde eliminating the arbitrary constants a and b

Answer 1

Answer:-

Eliminating the arbitrary constants a and b from z = a

2x+

b

2

y + ab.

Solution: Given z = a

2x + b

2

y + ab. (1)

Differentiating (1) partially w.r.t ‘x’

∂z

∂x = a

2

i.e., p = a

2

(2)

Differentiating (1) partially w.r.t ‘y

∂z

∂y = b

2

i.e., q = b

2

(3)

From (2) and (3)

a

2 = p and b

2 = q

Substituting in (1), we get z = px + qy +

√

pq