3-2 - March 2 2005 Announcements The last homework will not...

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March 2, 2005 Announcements: The last homework will not be collected. K. Ross has changed her office hours for the rest of the quarter to Monday 4:30pm-5:30pm MSC, and Wednesday 4:30pm-5:30pm MSC. Today § 9.3 Separable equations and mixing problems
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A separable equation is a first order dif- ferential equation in which the expression for dy dx can be factored as a function of x times a function of y , i.e. dy dx = g ( x ) f ( y ) . If f ( y ) = 0 let h ( y ) = 1 f ( y ) , then dy dx = g ( x ) h ( y ) . Hence h ( y ) dy = g ( x ) dx. Integrating on both sides we have h ( y ) dy = g ( x ) dx.
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§ 9.3 Problem # 16: Find the solution of the differential equation that satisfies the given initial condition. dy dt = t e y , y (1) = 0 .
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Mixing Problems (typical situation: chem- ical dissolved in water). Let r in and r out be the rates (in liters per minute) at which the liquid is entering and leaving the container respectively. Let C in and C out be the concentrations of chemicals entering and leaving the con- tainer respectively.
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