Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor Then solve the equation. μ(x, y) = 1 xy5*

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Show that the differential equation x¹y³ + x(1+y¹)y' = 0_ is not
exact, but becomes exact when multiplied by the integrating factor
Then solve the equation.
μ(x, y)
=
1
xy5*
The given equation is not exact, because My :
which is different from N =
1+y4
0
5 x² y
After multiplication with u(x, y), the equation is exact, because then
My = N₂ =
-
The general solution of the differential equation is given implicitly by
=
c, for any constant c, where y
+04 In y
Transcribed Image Text:Show that the differential equation x¹y³ + x(1+y¹)y' = 0_ is not exact, but becomes exact when multiplied by the integrating factor Then solve the equation. μ(x, y) = 1 xy5* The given equation is not exact, because My : which is different from N = 1+y4 0 5 x² y After multiplication with u(x, y), the equation is exact, because then My = N₂ = - The general solution of the differential equation is given implicitly by = c, for any constant c, where y +04 In y
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