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In exercises 1-10, classify each of the following integral equations as Fredholm or Volterra integral equation, linear or nonlinear, and homogeneous or nonhomogeneous: (1) u(x) = x+ (2) u(x) = 1 + x² + (3) u(x) = dt fatu(t) d S² (₂ = et + (4) u(x) = [²(x - 1)² u(t) dt 2 (5) u(2) = 2 + [atu (7) u(x) = 1 + (x - t)u(t) dt tu² (t) dt x 3 1 (6) u(z) = 2 + + √(x-1)³ u(t) dt 5 1 1 x+tu(t) xtu(t) dt dt

In exercises 1-10, classify each of the following integral equations as Fredholm or Volterra integral equation, linear or nonlinear, and homogeneous or nonhomogeneous: (1) u(x) = x+ (2) u(x) = 1 + x² + (3) u(x) = dt fatu(t) d S² (₂ = et + (4) u(x) = [²(x - 1)² u(t) dt 2 (5) u(2) = 2 + [atu (7) u(x) = 1 + (x - t)u(t) dt tu² (t) dt x 3 1 (6) u(z) = 2 + + √(x-1)³ u(t) dt 5 1 1 x+tu(t) xtu(t) dt dt

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In exercises 1-10, classify each of the following integral equations as Fredholm or Volterra integral equation, linear or nonlinear, and homogeneous or nonhomogeneous: (1) u(x) = x + (2) u(x) = 1 + x² + √(x − t)u(t) dt - (3) u(x) = e² + ² tu²³ (t) dt 3 (6) u(x) = ² So (4) u(x) = f (x - t)² u(t) dt (5) u(x) = ²/2 + (¹xtu(t) dt (7) u(x) = 1 + xtu(t) dt (10) u(x) = 1 x+ 5+ x 3 6 (x-1)³ u(t) dt 1 = 1- 1 x+tu(t) /0 (8) u(x) = = = cos x + ²/2 √² cos x u(t) dt [²* (x − 1)² u² (1) dt (9) u(x) = 1 + 10 dt - 5²(x - t)u(t) dt
Transcribed Image Text:In exercises 1-10, classify each of the following integral equations as Fredholm or Volterra integral equation, linear or nonlinear, and homogeneous or nonhomogeneous: (1) u(x) = x + (2) u(x) = 1 + x² + √(x − t)u(t) dt - (3) u(x) = e² + ² tu²³ (t) dt 3 (6) u(x) = ² So (4) u(x) = f (x - t)² u(t) dt (5) u(x) = ²/2 + (¹xtu(t) dt (7) u(x) = 1 + xtu(t) dt (10) u(x) = 1 x+ 5+ x 3 6 (x-1)³ u(t) dt 1 = 1- 1 x+tu(t) /0 (8) u(x) = = = cos x + ²/2 √² cos x u(t) dt [²* (x − 1)² u² (1) dt (9) u(x) = 1 + 10 dt - 5²(x - t)u(t) dt
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