MAT244H1- Midterm Exam Guide - Comprehensive Notes for the exam ( 34 pages long!)
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MAT244H1 Full Course Notes
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A differential equation is an equation involving some hypothetical function and its derivatives. As such, the differential equation is a description of some function (exists or not). A solution to a differential equation is a function that satisfies the differential equation. 3 + x y x is a solution to y y x. Some differential equations are famous/important: y = y = xe y axe y = y = ay. 0=+ y y y cos x y ay. Recall that a differential equation describes a phenomenon in terms of changes. A pool contains v liters of water which contains m kg of salt. Pure water enters the pool at a constant rate of v liters per minute, and after mixing, exits at the same rate. Write a differential equation that describes the density of salt in the pool at an arbitrary time t. ( )t : let, to model change in v. 1 be the density at time t. then.