MATH225 Lecture Notes - Lecture 4: Talking Lifestyle 1278, Lincoln Near-Earth Asteroid Research, Binomial Theorem

• School: University of Waterloo
• Department: Mathematics
• Course: MATH225
• Professor: unknown

Document Summary

0 is called an exact differential equation if there exists a function of two variables u(x,y) with continuous partial derivatives such that du x y m x y dx n x y dy. The general solution of an exact equation is given by u x y f y dy c. N x y have continuous partial derivatives in a certain domain d. M x y dx n x y dy. Is an exact equation if and only if. Algorithm for solving an exact differential equation: first it"s necessary to make sure that the differential equation is exact using the test for exactness: N x the given equation is exact terms of n not containing x dy c c. 2 c x y x y x y ( 5 ) y. ) (cid:160)is function of x alone , say f x then i f e f x dx.