Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n in x and y. Show that the general solution of Mdx + Ndy 0 is xM + yN = C For what value/s of n will this be valid?

Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n in x and y. Show that the general solution of Mdx + Ndy 0 is xM + yN = C For what value/s of n will this be valid?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 44E

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Suppose that Mdx + Ndy = 0 is an exact equation, and M and N are both homogenous functions of
degree n in x and y.
Show that the general solution of Mdx + Ndy = 0 is
xM + yN = C
For what value/s of n will this be valid?

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