Which method should be used to solve this D.E.?

Jeff12341234

e^x²=t^-1e^x²-[itex]\frac{1}{tx}[/itex][itex]\frac{dt}{dx}[/itex]

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:
[itex] \frac{dt}{dx}=xe^{x^2}(1-t)[/itex]

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.

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Jeff12341234	Which method should be used to solve this D.E.? Tweet e^x²=t^-1e^x²-[itex]\frac{1}{tx}[/itex][itex]\frac{dt}{dx}[/itex] 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: [itex] \frac{dt}{dx}=xe^{x^2}(1-t)[/itex] It is linear as well as separable.

Mark44 Mentor	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.