# Download e-book for iPad: Advanced Engineering Mathematics, 6th Edition by Peter V. O'Neil

By Peter V. O'Neil

ISBN-10: 0495082376

ISBN-13: 9780495082378

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**Additional resources for Advanced Engineering Mathematics, 6th Edition **

**Example text**

Use the initial condition to solve for the constant of integration. 12. y = 2x y 2 = 1 13. y = e −x In each of Problems 21 through 26, generate a direction field and some integral curves for the differential equation. Also draw the integral curve representing the solution of the initial value problem. These problems should be done by a software package. 21. y = sin y y 1 = /2 22. y = x cos 2x − y y 1 = 0 23. y = y sin x − 3x2 y 0 = 1 y 0 =2 24. y = ex − y y −2 = 1 14. y = 2x + 2 y −1 = 1 15. y = 4 cos x sin x y 25.

This process is called mathematical modeling. The model consists of the differential equation and other relevant information, such as initial conditions. We look for a function satisfying the differential equation and the other information, in the hope of being able to predict future behavior, or perhaps better understand the process being considered. 2 PROBLEMS In each of Problems 1 through 10, determine if the differential equation is separable. If it is, find the general solution (perhaps implicitly defined).

As an example, suppose a tank contains 200 gallons of brine (salt mixed with water), in which 100 pounds of salt are dissolved. A mixture consisting of 18 pound of salt per gallon is flowing into the tank at a rate of 3 gallons per minute, and the mixture is continuously stirred. 11). How much salt is in the tank at any time? 11 Before constructing a mathematical model, notice that the initial ratio of salt to brine in the tank is 100 pounds per 200 gallons, or 21 pound per gallon. Since the mixture pumped in has a constant ratio of 18 pound per gallon, we expect the brine mixture to dilute toward the incoming ratio, with a “terminal” amount of salt in the tank of 18 pound per gallon, times 200 gallons.

### Advanced Engineering Mathematics, 6th Edition by Peter V. O'Neil

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