Question

b) Solve the partial differential equation
r - 3s + 2t - p + 2q = (2 + 4x)e-Y​

Answer 1

Answer:

Step-by-step explanation:

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.