lecture 4 first order dierential equations and the fundamental theorem of calculus we ll now begin to develop techniques for solving rst order dierential equations the general problem is this ...
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...Lecture first order dierential equations and the fundamental theorem of calculus we ll now begin to develop techniques for solving rst general problem is this given a equation dy f x y dx find function such that substituted on both sides resulting mathematical identity unfortunately not solve in generality stated rather will have proceed special case by end however up with substantial repetoire enable us all but most pathological form simplest when right hand side alone so let consider equivalent answering question what has as its derivative addressing was actually large part i ii contex it phrased anti answer be essentially same nd solutions e integrating there are some additional nuances details lled thisishalldobelow towritedownthesolutionofthisequation itsucestosimplyapplythefundamental roughly speaking says integrals derivatives inverses each other here more precise statement continuous z n lim xf ix then dierentiable b df if any whose equal digression denite indenite constants in...