Show that the differential equation x*y + x(1+ y*)y' = 0 _is not exact, but becomes exact when multiplied by the integrating factor μ (π, ) 1 Then solve the equation. xy3* The given equation is not exact, because My = which is different from NV. After multiplication with u(x, y), the equation is exact, because then My = N = The general solution of the differential equation is given implicitly by = c, for any constant c.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
,23
Show that the differential equation xy + x(1+y²)y' = 0 is not
exact, but becomes exact when multiplied by the integrating factor
1
Then solve the equation.
xy³'
µ(x, y)
The given equation is not exact, because M,
which is different from ,
After multiplication with u(x, y), the equation is exact, because then
My = N. =
The general solution of the differential equation is given implicitly by
= c, for any constant c.
Transcribed Image Text:,23 Show that the differential equation xy + x(1+y²)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor 1 Then solve the equation. xy³' µ(x, y) The given equation is not exact, because M, which is different from , After multiplication with u(x, y), the equation is exact, because then My = N. = The general solution of the differential equation is given implicitly by = c, for any constant c.
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