Not Understanding This Simplification

  • Thread starter snowJT
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  • #1
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I feel dumb because I can't see how you get from this:

[tex]x \frac{dy}{dx}+x^2y+y=0[/tex]

to this

[tex]\frac{dy}{dx}+(x+\frac{1}{x})y=0[/tex]

this is what I would of thought it would be...

[tex]\frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0[/tex]

no?
 

Answers and Replies

  • #2
cristo
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Why do you think it should be [tex]\frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0[/tex]?

Divide the original equation by x; what do you get?
 
  • #3
arildno
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Factorize [itex]x^{2}y+y[/itex] in the simplest manner.
What do you get?
 
  • #4
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Why do you think it should be [tex]\frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0[/tex]?

Divide the original equation by x; what do you get?
you get [tex]\frac{dy}{dx}+(\frac{x^2}{x}+\frac{y}{x})+\frac{y}{x}=0[/tex]

Factorize [itex]x^{2}y+y[/itex] in the simplest manner.
What do you get?
you get [tex]\frac{x^2}{y}+1[/tex]
 
  • #5
arildno
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No, you don't.

What does it mean to FACTORIZE?
 
  • #6
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[tex]y(x^2+1)[/tex]

oh I see now... thanks

but why are you not dividing the y thats on the most right side of the LHS by x?
 
  • #7
arildno
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So, you have now your diff.eq in the form:
[tex]x\frac{dy}{dx}+(x^{2}+1)y=0[/tex]
Multiply this equation with 1/x; what do you get?
 
  • #8
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sorry, I see it now... I'm just really bad at these things...
 

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