Not Understanding This Simplification

[snowJT]

I feel dumb because I can't see how you get from this:

x \frac{dy}{dx}+x^2y+y=0

to this

\frac{dy}{dx}+(x+\frac{1}{x})y=0

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

\frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0

no?

 

[cristo]

Why do you think it should be \frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0?

Divide the original equation by x; what do you get?

 

[arildno]

Factorize x^{2}y+y in the simplest manner.
What do you get?

 

[snowJT]

Why do you think it should be \frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0?

Divide the original equation by x; what do you get?

you get \frac{dy}{dx}+(\frac{x^2}{x}+\frac{y}{x})+\frac{y}{x}=0

Factorize x^{2}y+y in the simplest manner.
What do you get?

you get \frac{x^2}{y}+1

 

[arildno]

No, you don't.

What does it mean to FACTORIZE?

 

[snowJT]

y(x^2+1)

oh I see now... thanks

but why are you not dividing the y that's on the most right side of the LHS by x?

 

[arildno]

So, you have now your diff.eq in the form:
x\frac{dy}{dx}+(x^{2}+1)y=0
Multiply this equation with 1/x; what do you get?

 

[snowJT]

sorry, I see it now... I'm just really bad at these things...