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