Solving for a Differential Equation with Inspection.

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Homework Help Overview

The discussion revolves around solving a differential equation through inspection. The original poster expresses difficulty in approaching the problem and shares their attempts at manipulation of the equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the manipulation of the equation, with the original poster attempting to rearrange terms and questioning how to handle specific components. Others suggest considering the roles of m and n, and one participant notes that ignoring certain terms may lead to an exact equation.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations and approaches. Some guidance has been offered regarding the flexibility of manipulating the equation, but no consensus or clear direction has emerged yet.

Contextual Notes

The original poster mentions feeling stuck and lacking confidence in their ability to solve the problem by inspection. There is also a sense of uncertainty regarding the roles of m and n in the equation.

Kiziaru
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I'm rather bad at solving by inspection, and right now I am stuck on a problem I can't solve.1.http://www.texify.com/img/%5CLARGE%5C%21y%28x%5E2y%5E2-m%29dx%2Bx%28x%5E2y%5E2%2Bn%29dy%3D0.gif
2.The attempt at a solution
http://www.texify.com/img/%5CLARGE%5C%21x%5E2y%5E3dx-mdx%2Bx%5E3y%5E2dy%2Bndy%3D0.gif

Rearrange and divide by x^2 * y^2

http://www.texify.com/img/%5CLARGE%5C%21ydx%2Bxdy%20%3D%20%28mydx-nxdy%29/x%5E2y%5E2.gif

I know that xdy+ydx = d(xy) buy I don't know what to do with the other side. If I try to make the right side into d(mx/ny) I'm left over with an x^2 that I don't know how to get rid of.
 
Last edited by a moderator:
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Welcome to PF!

Hi Kiziaru! Welcome to PF! :smile:

(I haven't actually tried to solve this :redface:, but …)

my immediate reaction on seeing that m and n was to think "xm and yn"
 


tiny-tim said:
Hi Kiziaru! Welcome to PF! :smile:

(I haven't actually tried to solve this :redface:, but …)

my immediate reaction on seeing that m and n was to think "xm and yn"

Thanks! I've always lurked on this site, but I never posted because most of what I needed help with was already answered, until today. :frown:

Also, I hate to sound dumb, but what wizardry is this? How can I make m and n into exponents? And is this part of a plan to get d(arctan(y/x))?
 
Kiziaru said:
How can I make m and n into exponents? And is this part of a plan to get d(arctan(y/x))?

no specific plan … just a vague idea :smile:

remember, you can multiply the whole equation by anything you like :wink:
 
What I see is that if you ignore the terms with m and n, the other part is exact...
 

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