Is This Differential Equation Separable?

[Jeff12341234]

e^x2=t^-1e^x2-\frac{1}{tx}\frac{dt}{dx}

Which method should be used and how can you tell just by looking at it?

 

[bigfooted]

you check if the equation has a form that is easy to solve: linear, exact, separable, some others that are more difficult...

So, you start by rewriting the equation:
\frac{dt}{dx}=xe^{x^2}(1-t)

It is linear as well as separable.

 

[Mark44]

To add to what bigfooted said, checking the equation for separability is one of the easier things to do, so that's one of the things you should do first.

If it turns out that an equation isn't separable, at least you haven't spend much time in checking.