Explanation Given: The differential equation is x 3 d y d x + 2 x 2 y = 10 sin x with the initial condition y ( 1 ) = 0 . The sine integral function is defined as, Si ( x ) = ∫ 0 x sin t t d t (1) Where the integrand is defined to be 1 at x = 0 . Procedure used: The standard form of the first order linear differential equation with initial condition y ( x 0 ) = y 0 is, d y d x + P ( x ) y = Q ( x ) (2) To solve the equation (2) for y ( x ) , use the integrating factor method. The integrating factor of the differential equation is e ∫ P ( x ) d x . And the solution of the differential equation is, y ⋅ ( Integrating factor ) = ∫ ( ( Integrating factor ) ⋅ ( Q ( x ) ) ) d x + C (3) Here, C is constant. Calculation: The differential equation with initial condition y ( 1 ) = 0 is, x 3 d y d x + 2 x 2 y = 10 sin x d y d x + 2 x 2 y x 3 = 10 sin x x 3 d y d x + 2 y x = 10 sin x x 3 (4) Compare equation (4) with equation (2). P ( x ) = 2 x and Q ( x ) = 10 sin x x 3 Therefore the integrating factor of the differential equation (4) is, I . F = e ∫ 2 x d x = x 2 Substitute x 2 for integrating factor and 10 sin x x 3 for Q ( x ) in equation (3)

First Course in Differential Equations (Instructor's)

11th Edition

ISBN: 9781305965775

Author: ZILL

Publisher: CENGAGE L

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 2.3, Problem 47E

To determine

The solution in the terms of Si(x).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.3, Problem 46E

Chapter 2.3, Problem 48E

Students have asked these similar questions

Page < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.

13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of the following sets and the cardinal number of each set. a) W° and n(W) b) (VUW) and n((V U W)') c) VUWUX and n(V U W UX) d) vnWnX and n(V WnX)

9) Use the Venn Diagram given below to determine the number elements in each of the following sets. a) n(A). b) n(A° UBC). U B oh a k gy ท W z r e t ་ C

Chapter 2 Solutions

First Course in Differential Equations (Instructor's)

Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...

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 in the terms of Si ( x ) .

Solution Summary: The author explains the solution of the initial value problem in terms of Si(x).

Concept explainers

Videos

The solution in the terms of Si(x).

Want to see the full answer?

Chapter 2 Solutions