Solving Separable DE with Initial Value: Techniques and Examples

[Jeann25]

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

y'=xy/(1+x²)

 

[arildno]

Why doesn't that work?

 

[d_leet]

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]

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]

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]

Nevermind. I get it now. Thank you :)