By Peter V O'Neil
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Extra resources for Advanced engineering mathematics
1/x + y + (3y + x)y = 0 2 In each of Problems 6 and 7, determine α so that the equation is exact. Obtain the general solution of the exact equation. 6. 3x 2 + x y α − x 2 y α−1 y = 0 7. 2x y 3 − 3y − (3x + αx 2 y 2 − 2αy)y = 0 In each of Problems 8 through 11, determine if the differential equation is exact in some rectangle containing the point where the initial condition is given. If it is exact, solve the initial value problem. If not, do not attempt a solution. 9. 3y 4 − 1 + 12x y 3 y = 0; y(1) = 2 11.
How long will it take the container to empty? This is a simple enough problem for something like a soda can, but it is not so easy with a large storage tank (such as the gasoline tank at a service station). Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.
The initial ratio of salt to brine in the tank is 100 pounds per 200 gallons or 1/2 pound per gallon. Since the mixture pumped in has a constant ratio of 1/8 pound per gallon, we expect the brine mixture to dilute toward the incoming ratio with a terminal amount of salt in the tank of 1/8 pound per gallon times 200 gallons. This leads to the expectation (in the long term) that the amount of salt in the tank should approach 25, as the model verifies. 2 PROBLEMS In each of Problems 1 through 5, find the general solution.
Advanced engineering mathematics by Peter V O'Neil