Integrating Factor Show that the differential equation is exact only when For show that

Chapter 16, Problem 38

(choose chapter or problem)

Integrating Factor Show that the differential equation

\(\left(a x y^{2}+b y\right) d x+\left(b x^{2} y+a x\right) d y=0\)

is exact only when a = b. For \(a \neq b\), show that \(x^{m} y^{n}\) is an integrating factor, where

\(m=-\frac{2 b+a}{a+b}, \quad n=-\frac{2 a+b}{a+b}\).

Text Transcription:

(axy^2+by)dx+(bx^2y+ax)dy=0

a neq b

x^m y^n

m=-2b+a/a+b, n=-2a+b/a+b