Explanation Formula used: The integral of sine function is: ∫ e x = e x + C Calculation: The given ODE is y ′ + x e − x 2 2 = 0 . Rewrite the function as, y ′ = − x e − x 2 2 . This implies, d y d x = − x e − x 2 2 d y = − x e − x 2 2 d x Let u = − x 2 2 . This implies d u = − 2 x d x 2 = − x d x . Integrate and find the solution of ODE as follows

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Videos

Question

Chapter 1.1, Problem 2P

To determine

The solution of ODE by integration or by differentiation y′+xe−x22=0.

Expert Solution & Answer

Learn your wayIncludes step-by-step video

See solution

Check out sample textbook solution

03:02

Chapter 1.1, Problem 1P

Chapter 1.1, Problem 3P

Students have asked these similar questions

Page of 2 ZOOM + 1) Answer the following questions by circling TRUE or FALSE (No explanation or work required). i) If A = [1 -2 1] 0 1 6, rank(A) = 3. (TRUE FALSE) LO 0 0] ii) If S = {1,x,x², x³} is a basis for P3, dim(P3) = 4 with the standard operations. (TRUE FALSE) iii) Let u = (1,1) and v = (1,-1) be two vectors in R². They are orthogonal according to the following inner product on R²: (u, v) = U₁V₁ + 2U2V2. ( TRUE FALSE) iv) A set S of vectors in an inner product space V is orthogonal when every pair of vectors in S is orthogonal. (TRUE FALSE) v) Dot product of two perpendicular vectors is zero. (TRUE FALSE) vi) Cross product of two perpendicular vectors is zero. (TRUE FALSE) 2) a) i) Determine which function(s) are solutions of the following linear differential equation. - y (4) — 16y= 0 • 3 cos x • 3 cos 2x -2x • e • 3e2x-4 sin 2x ii) Find the Wronskian for the set of functions that you found from i) as the solution of the differential equation above. iii) What does the result…

please help

1. Give a subset that satisfies all the following properties simultaneously: Subspace Convex set Affine set Balanced set Symmetric set Hyperspace Hyperplane 2. Give a subset that satisfies some of the conditions mentioned in (1) but not all, with examples. 3. Provide a mathematical example (not just an explanation) of the union of two balanced sets that is not balanced. 4. What is the precise mathematical condition for the union of two hyperspaces to also be a hyperspace? Provide a proof. edited 9:11

Chapter 1 Solutions

Name: The solution of ODE by integration or by differentiation y ′ + x e − x 2 2 = 0 .
Uploaded: 2022-01-27
Channel: Bartleby
Description: Explanation Formula used: The integral of sine function is: ∫ e x = e x + C Calculation: The given ODE is y ′ + x e − x 2 2 = 0 . Rewrite the function as, y ′ = − x e − x 2 2 . This implies, d y d x = − x e − x 2 2 d y = − x e − x 2 2 d x Let u = − x 2 2 . This implies d u = − 2 x d x 2 = − x d x . Integrate and find the solution of ODE as follows

Advanced Engineering Mathematics

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

Knowledge Booster

$Advanced Math$

Learn more about

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