A First Course in Differential Equations with Modeling Applications (MindTap Course List)

11th Edition

ISBN: 9781337515573

Author: ZILL

Publisher: Cengage

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Textbook Question

Chapter 4.1, Problem 26E

In Problems 23–30 verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution.

26. 4 y ″ − 4 y ′ + y = 0 ; e x / 2 , x e x / 2 , ( − ∞ , ∞ )

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Chapter 4.1, Problem 25E

Chapter 4.1, Problem 27E

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Chapter 4 Solutions

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Given that x(t) = c1 cos t + c2 sin t is the...Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

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In Problems 23–30 verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution. 26. 4 y ″ − 4 y ′ + y = 0 ; e x / 2 , x e x / 2 , ( − ∞ , ∞ )

Solution Summary: The author explains how the functions y_1=ex2, , and form a fundamental set of solutions of the differential equation.

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Chapter 4 Solutions