Solving Separable DE with Initial Value: Techniques and Examples

Jeann25 · Mar 12, 2006

How would I start this one? I tried dividing by y, but that does not work

y'=xy/(1+x²)

arildno · Mar 12, 2006

Why doesn't that work?

d_leet · Mar 12, 2006

Jeann25 said:

How would I start this one? I tried dividing by y, but that does not work

y'=xy/(1+x²)

Yeah why does dividing by y not work?

Jeann25 · Mar 12, 2006

Here's what I did:

1/y y' = x/(1+x²)
ln y = 1/2 ln (1+x²)+c
y = ce^(1/2 ln(1+x²))

Answer's supposed to be: c*sqrt(1+x²)

d_leet · Mar 12, 2006

Jeann25 said:

Here's what I did:

1/y y' = x/(1+x²)
ln y = 1/2 ln (1+x²)+c
y = ce^(1/2 ln(1+x²))

Answer's supposed to be: c*sqrt(1+x²)

Yeah, ok and how is that different from what you had? Just simplify your expression with the properties of logs.

Jeann25 · Mar 12, 2006

Nevermind. I get it now. Thank you :)

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