Explanation Formula used: The adjoint of the differential equation of the form P ( x ) y ″ + Q ( x ) y ′ + R ( x ) y = 0 is given by P v ″ + ( 2 P ′ − Q ) v ′ + ( P ″ + Q ′ + R ) v = 0 . Calculation: Consider the differential equation of the form P ( x ) y ″ + Q ( x ) y ′ + R ( x ) y = 0 . The adjoint of P ( x ) y ″ + Q ( x ) y ′ + R ( x ) y = 0 is P μ ″ + ( 2 P ′ − Q ) μ ′ + ( P ″ + Q ′ + R ) μ = 0 . Compare the above equation with P ( x ) y ″ + Q ( x ) y ′ + R ( x ) y = 0 and obtain the values of P ( x ) , P ′ ( x ) , P ″ ( x ) , Q ( x To determine To check: Whether the given equations are self adjoint.

Elementary Differential Equations and Boundary Value Problems, Enhanced

11th Edition

ISBN: 9781119381648

Author: Boyce

Publisher: WILEY

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Chapter 3.2, Problem 38P

To determine

To show: The equation P(x)y″+Q(x)y′+R(x)y=0 is self adjoint if P′(x)=Q(x).

To determine

To check: Whether the given equations are self adjoint.

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Chapter 3.2, Problem 37P

Chapter 3.3, Problem 1P

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Chapter 3 Solutions

Elementary Differential Equations and Boundary Value Problems, Enhanced

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