Given a differential equation M(x, y) + N(x, y) = 0. Suppose (N₁ - dx y)/M is a function of y only, i.e., (N₂ - My)/M = g(y) for some function g. Let μ(y) = exp (√[9(1) dy). g(y) how that µ(y)M + µ(y)Ndy = 0 is an exact equation. dx

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4.
ay
dx
Given a differential equation M(x, y) + N(x, y) = 0. Suppose (Na-
My)/M is a function of y only, i.e., (Nz - My)/M = g(y) for some function g. Let
μ(y) = exp
g(y) dy
Show that µ(y)M +µ(y) N dy = 0 is an exact equation.
dx
-
Transcribed Image Text:4. ay dx Given a differential equation M(x, y) + N(x, y) = 0. Suppose (Na- My)/M is a function of y only, i.e., (Nz - My)/M = g(y) for some function g. Let μ(y) = exp g(y) dy Show that µ(y)M +µ(y) N dy = 0 is an exact equation. dx -
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