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Unformatted text preview: Review Differential equations, Classification, Com plete Solution (Reduction to Integration) of FOLODE, Existence and Uniqueness Theorem for the general FOODE, Sepa rable FOODE. Example: The FOODE dy dx = x 2 1 y 2 can be rewritten as x 2 dx +( y 2 1) dy = 0 and x 3 / 3+ y 3 / 3 y = c . This is a cubic equation for y , so all we can say is that the integral curves y ( x ) of the solutions all satify x 3 / 3 + y 3 ( x ) / 3 y ( x ) = c . c a constant. 2 Applications of FOODE Example: A tank contains G gallons of water in which are dissolved initially S pounds of salt. Water of salinity s [lb/gal] is added at the rate r [gal/min]. The so lution leaves the tank at the same rate r . flowratein: r [gal/min] salinity of inflow: s [lb/gal] flowrateout: r [gal/min] S lb Salt at time 0 G gallons saline solution What is the amount of salt in the tank at any given time t ? 3 Applications of FOODE Example: A tank contains G gallons of water in which are dissolved initially S pounds of salt. Water of salinitypounds of salt....
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This note was uploaded on 09/07/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas.
 Spring '08
 Turner

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