Show that the differential equation x²y³ + x(1+y²)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor 1 μ(x, y) Then solve the equation. = xy ³* The given equation is not exact, because My = which is different from N = After multiplication with u(x, y), the equation is exact, because then My = Nx = The general solution of the differential equation is given implicitly by = c, for any constant c, where y > 0.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Show that the differential equation x²y³ + x(1+y²)y' = 0 is not
exact, but becomes exact when multiplied by the integrating factor
1
μ(x, y)
Then solve the equation.
=
xy ³*
The given equation is not exact, because My
=
which is different from N
=
After multiplication with u(x, y), the equation is exact, because then
My = Nx =
The general solution of the differential equation is given implicitly by
= c, for any constant c, where y > 0.
Transcribed Image Text:Show that the differential equation x²y³ + x(1+y²)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor 1 μ(x, y) Then solve the equation. = xy ³* The given equation is not exact, because My = which is different from N = After multiplication with u(x, y), the equation is exact, because then My = Nx = The general solution of the differential equation is given implicitly by = c, for any constant c, where y > 0.
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