n mFind an integrating factor of the form x^y" and solve the equation.(2y²-12xy)dx + (4xy - 12x²)dy=0An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant, andmultiplying by the integrating factor.(Type an expression using x and y as the variables.)no solutions were lostthe solution y = 0 was lostthe solution x = 0 was lostby

Answered: n m Find an integrating factor of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

n m
Find an integrating factor of the form x^y" and solve the equation.
(2y²-12xy)dx + (4xy - 12x²)dy=0
An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant, and
multiplying by the integrating factor.
(Type an expression using x and y as the variables.)
no solutions were lost
the solution y = 0 was lost
the solution x = 0 was lost
by

Expert Solution

Step 1

Given

$(2 y^{2} - 12 x y) d x + (4 x y - 12 x^{2}) d y = 0$

compare to $M d x + N d y = 0$

Here

$M = 2 y^{2} - 12 x y \frac{\partial M}{\partial y} = 4 y - 12 x N = 4 x y - 12 x^{2} \frac{\partial N}{\partial x} = 4 y - 24 x T h e r e f o r e, \frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x} T h e g i v e n D i f f e r e n t i a l e q u a t i o n i s n o t e x a c t .$