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I'm learning differential equations, and although I understand the methods I have learned thus far, I often have trouble seeing what is the reasoning behind them.

Take for example, the use of the integrating factor when solving first order linear ODE's. I understand how to use it, but i'm not sure where it came from. In the resources that i'm using there's really not explanation, instead the discussion is limited to: assume there's a function by which we can multiply our differential equation to make it integrable.

Can anybody explain why we use this approach?

thanks,

Erik

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# Integrating Factor

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