Transcription of First-Order Differential Equations and Their Applications
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First-Order Differential Equations and Their Applications
CHAPTER 1 First-Order Differential Equations and Their Introduction to Ordinary Differential EquationsDifferential Equations are found in many areas of mathematics, science, and engineer-ing. Students taking a first course in Differential Equations have often already seensimple examples in Their mathematics, physics, chemistry, or engineering courses. Ifyou have not already seen Differential Equations , go to the library or Web and glanceat some books or journals in your major field. You may be surprised to see the wayin which Differential Equations dominate the study of many aspects of science mathematicsinvolves the relationships between mathematics and itsapplications. Often the type of mathematics that arises in Applications is differentialequations.
First-Order Differential Equations and Their Applications 5 Example 1.2.1 Showing That a Function Is a Solution Verify that x=3et2 is a solution of the first-order differential equation dx dt =2tx. (2) SOLUTION.Wesubstitutex=3et 2 inboththeleft-andright-handsidesof(2). On the left we get d dt (3e t2)=2t(3e ), using the chain rule.Simplifying the right-hand
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