Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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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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Chapter 5.2, Problem 8E

In Problems 3-18, use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t .

( D − 3 ) [ x ] + ( D − 1 ) [ y ] = t ,

( D + 1 ) [ x ] + ( D + 4 ) [ y ] = 1

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Chapter 5.2, Problem 7E

Chapter 5.2, Problem 9E

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In case an equation is in the form y = f(ax+by+c), i.e., the RHS is a linear function of x and y. We will use the substitution = ax + by + c to find an implicit general solution. The right hand side of the following first order problem y = (4x − 3y + 1) 5/6 +, y(0) = 0 is a function of a linear combination of x and y, i.e., y = f(ax +by+c). To solve this problem we use the substitution v= ax + by + c which transforms the equation into a separable equation. We obtain the following separable equation in the variables x and v: U' = Solving this equation an implicit general solution in terms of x, u can be written in the form x+ Transforming back to the variables x and y the above equation becomes x+ = C. y = = C. Next using the initial condition y(0) = 0 we find C = 6 Then, after a little algebra, we can write the unique explicit solution of the initial value problem as

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Chapter 5 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

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In Problems 3-18 , use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t . ( D − 3 ) [ x ] + ( D − 1 ) [ y ] = t , ( D + 1 ) [ x ] + ( D + 4 ) [ y ] = 1

Solution Summary: The author explains that the standard operator form of the linear system is given by rll(D-3)

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