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Let a(x) and b(y) be positive functions. Suppose the ODE dy M(x, y) + N(x, y) · = 0 dx is exact vith M (x, y) = a(x)g(y) and N(x, y) = f(x)b(y). Show that there is a real %3D constant c and such that f'(x) = c · a(x) and g'(y) = c · b(y). %3D

Let a(x) and b(y) be positive functions. Suppose the ODE dy M(x, y) + N(x, y) · = 0 dx is exact vith M (x, y) = a(x)g(y) and N(x, y) = f(x)b(y). Show that there is a real %3D constant c and such that f'(x) = c · a(x) and g'(y) = c · b(y). %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let a(x) and b(y) be positive functions. Suppose the ODE dy Miz, ) + N(τ, y) . dx %3D is exact, with M(x, y) a(x)g(y) and N(x, y) = f(x)b(y). Show that there is a real constant c and such that f'(x) = c - a(x) and g'(y) = c · b(y). %3D %3D
Transcribed Image Text:Let a(x) and b(y) be positive functions. Suppose the ODE dy Miz, ) + N(τ, y) . dx %3D is exact, with M(x, y) a(x)g(y) and N(x, y) = f(x)b(y). Show that there is a real constant c and such that f'(x) = c - a(x) and g'(y) = c · b(y). %3D %3D
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