- #1
Square1
- 143
- 1
So I just learned about these integrating factors and their utility in solving first order linear differential equations today. My mind is just kind of blown how it ends up simplifying the integration so much. Thats really pretty much the main thing I wanted to say... lol.
But also, how the hell are these kind of techniques discovered? Really (thats second question). Are they fluke coincidences that people just notice, "oh look multiply by e^integral of this P(x) through the expression and finding an answer to the equation is way easier!" Or is it more conscious implementation of some strategy, or noticing algebraic patterns. Anyone know about the history here? Is this all part ol Newtons package that he came up with? Sorry if the newbishness here is making some of you cringe lol. But i am just really amazed by this stuff.
Cheers
But also, how the hell are these kind of techniques discovered? Really (thats second question). Are they fluke coincidences that people just notice, "oh look multiply by e^integral of this P(x) through the expression and finding an answer to the equation is way easier!" Or is it more conscious implementation of some strategy, or noticing algebraic patterns. Anyone know about the history here? Is this all part ol Newtons package that he came up with? Sorry if the newbishness here is making some of you cringe lol. But i am just really amazed by this stuff.
Cheers