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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.

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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