MTH 425 Lecture : 1 1st order eqns
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Def"m a single if fan variable the fan is y. X is in called called yex dependent independent the the variable variable. First order order of the appearing in order. My ffx. gl on and write if thus a we have. Lhs consider day differentials dx my dy day dx can then we lyin as. Tix y waxy e y s satisfies the de as. Rts fan mix t day e ex y x e x yet ex. Mix any is of functions xtc constant called c a. Def"m general fonts family of solution a that satisfy one parameter. The de fix y views field in a in this field as a the xy plane field of slopes initial. De that value problem ivp preniribed patinfien a. Ivp the involved selecting the specific general solution which natinfies the hour a syntem changed no solving it possible evolutions initial specific state is prescribed possible evolution is then only solving an member.
