MATH 1ZB3 Lecture 14: 9.1 Ordinary Differential Equations
13 Mar 2019
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Odes anequation ie statementof variablederivatives thatcontains ordinary single containonlyone independent variable derivatives. E equation has anequalsign order gist e. g y sinx try focusonthis y d. 3edorder y sitiy cosx x"t 7 ty y. Orderofode eg y x highest derivative in ode solveby integration in fdd d fx dx anarbitraryconstant forseparable generalsolution callpossiblesolutions y. 3 3 y 1 youget afamilyofsolution eg y 1. For now whenyougetbeyondfirst orderdont trytosokeit 3 l g y t y o d. is cx asolution of this ode. Y sinx y costy sincx sin1mtsink or y ty. L willbegivingyouyoutest y cosi is aparticularsolution ej. iteeie ox y exisno asolution. Initial vane problems provide an initialvalueofy y y etc to choose a particular solution fromthegeneral eg ikerm y. Ifshefallswithinitialspeed of 0 initialposition10in findequationof height at the t. 12 asyouknow"d findode p i o is theode get p andp bytakingintegralstepbystep arbituoy sosigndon"t matter subininitialvalues. Not solving ode"s e. g y 5y 5y2 y g y understanding propertiesandeliminatingpossibilitiesofsolutions shakyconewith agraph knowy knowslopeofaspecific point.
