Answer to Question #231373 in Chemical Engineering for pavani

Question

5) Find the particular integral of ∂²z/∂x²-3 ∂²z/∂x∂y+∂²z/∂y²= 2x sin y.

Answer 1

Given equation can be written as 𝜕 2 𝑧 𝜕𝑥 2 = 1 𝑎 𝑥𝑦 ...(1) Integrating (1) w. r. t., 𝑥, we get 𝜕𝑧 𝜕𝑥 = 𝑦 𝑎 𝑥 2 2 + ∅1(y) ...(2) where ∅1(y) is an arbitrary function of y Integrating (2) w. r. t., x, z = 𝑦 𝑎 3 6 + x ∅1(y) + ∅2(y)

Multiplying (1) by 𝑥 we get 𝑥 𝜕𝑝 𝜕𝑥 + 𝑝 𝑥 = 9𝑥 2𝑦 3 ⇒ 𝑝𝑥 = 9 𝑥 2𝑦 3 𝑑𝑥 ⇒ 𝑝𝑥 = 9 𝑥 3𝑦 3 3 + 𝑓 𝑦 ⇒ 𝑝𝑥 = 3𝑥 3𝑦 3 + 𝑓