(a) Explanation The given differential equation is y ″ − x 2 y = 0 . It is known that the general solution of the differential equation of the form y ″ + 1 − 2 a x y ′ + ( b 2 c 2 x 2 c − 2 + a 2 − p 2 c 2 x 2 ) y = 0 , p ≥ 0 is given as follows: y = x a [ c 1 J p ( b x c ) + c 2 Y p ( b x c ) ] The general solution of the differential equation x 2 y ″ + x y ′ − ( α 2 x 2 + v 2 ) y = 0 is given by: y = c 1 I v ( α x ) + c 2 K v ( α x ) Compare the standard equation with the given equation to obtain the following result. 1 − 2 a x = 0 , b 2 c 2 x 2 c − 2 + a 2 − p 2 c 2 x 2 = − x 2 Now compare the above equations to obtain the value of the variables. 1 − 2 a = 0 , 2 c − 2 = 2 , b 2 c 2 = − β 2 c 2 = − 1 , a 2 − p 2 c 2 = 0 The value of a is calculated as follows: 1 − 2 a = 0 a = 1 2 The value of c is calculated as follows: 2 c − 2 = 2 (b) To determine The solution of the differential equation x y ″ + y ′ − 7 x 3 y = 0 in terms of the modified Bessel functions I n and K n , assuming b = β i , β > 0 .

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

11th Edition

ISBN: 9781305965720

Author: Dennis G. Zill

Publisher: Cengage Learning

See similar textbooks

Concept explainers

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…

Videos

Question

Chapter 6.4, Problem 22E

(a)

To determine

The solution of the differential equation y″−x2y=0 in terms of the modified Bessel functions In and Kn, assuming b=βi, β>0.

(b)

To determine

The solution of the differential equation xy″+y′−7x3y=0 in terms of the modified Bessel functions In and Kn, assuming b=βi, β>0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 21E

Chapter 6.4, Problem 23E

Students have asked these similar questions

Q/Find the Laurent series of (2-3) cos↓ around z = 1. 2-1

#1). A technique is given with 150 mAs is 40 kV and produces an EI value = 400. Find the new EI value, if mAs is 75 and 34 kV are used.

Q3: Answer the following: (i) Let f(z) is an analytic function in a simply connected domain S and y is a simple, closed, positively oriented contour lying in S. Prove that f, f(z)dz = 0.

Chapter 6 Solutions

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The solution of the differential equation y ″ − x 2 y = 0 in terms of the modified Bessel functions I n and K n , assuming b = β i , β > 0 .

Solution Summary: The author explains the solution of the differential equation y′′-x20 in terms of modified Bessel functions.

Concept explainers

Videos

The solution of the differential equation y″−x2y=0 in terms of the modified Bessel functions In and Kn, assuming b=βi, β>0.

The solution of the differential equation xy″+y′−7x3y=0 in terms of the modified Bessel functions In and Kn, assuming b=βi, β>0.

Want to see the full answer?

Chapter 6 Solutions

The solution of the differential equation y ″ − x 2 y = 0 in terms of the modified Bessel functions I n and K n , assuming b = β i , β &gt; 0 .

Solution Summary: The author explains the solution of the differential equation y′′-x20 in terms of modified Bessel functions.

Concept explainers

Videos

The solution of the differential equation y″−x2y=0 in terms of the modified Bessel functions In and Kn, assuming b=βi, β>0.

The solution of the differential equation xy″+y′−7x3y=0 in terms of the modified Bessel functions In and Kn, assuming b=βi, β>0.

Want to see the full answer?

Chapter 6 Solutions

The solution of the differential equation y ″ − x 2 y = 0 in terms of the modified Bessel functions I n and K n , assuming b = β i , β > 0 .