# Math Help - Separating differential equations?

1. ## Separating differential equations?

I have this question:is my answer right?

The way I found this was just by trying to separate each one and I had trouble with all of them but option 3. Which I separated into: y=C-cosx. Did I do something wrong or am I right to say that dy/dx=sinx is the answer for this?

(My friend taking the same practice quiz is saying that he thinks the second one is separable, but he doesn't know how to separate it!)

2. ## Re: Separating differential equations?

$\dfrac {dy}{dx}=\sin(x)$ is separable, but I also think that

$\dfrac {dy}{dx}=2\ln(x)y$ is separable as well

$\dfrac{dy}{y} = 2\ln(x) dx$

maybe it's supposed to be

$\dfrac{dy}{dx}=2\ln(xy)$

If that's the case then no, it's not separable either.

3. ## Re: Separating differential equations?

Originally Posted by romsek
$\dfrac {dy}{dx}=\sin(x)$ is separable, but I also think that

$\dfrac {dy}{dx}=2\ln(x)y$ is separable as well

$\dfrac{dy}{y} = 2\ln(x) dx$

maybe it's supposed to be

$\dfrac{dy}{dx}=2\ln(xy)$

If that's the case then no, it's not separable either.
Oh you're right! I automatically made it dy/dx=2ln(xy) but the other way could be separated..hm. Thanks!