Since the right-hand side of equation (36) is zero when r = ₁, conclude that t exp(r₁t) is also a solution of L[y] = 0. In each of Problems 18 through 22, use the method of reduction of order to find a second solution of the given differential equation. 18. 12y"-4ty' +6y=0, t> 0; 19. 12y" +2ty' - 2y = 0, t> 0; 20. t2y" + 3ty' + y = 0, t> 0; 21. xy" - y' +4x³y = 0, x > 0; y₁(t) = 1² y₁(t) = t y(t) = 1-¹ y₁(x) = sin(x²) 22 ll 11 for an 1-kc the coc nonneg = 0 t as t Thus w
Since the right-hand side of equation (36) is zero when r = ₁, conclude that t exp(r₁t) is also a solution of L[y] = 0. In each of Problems 18 through 22, use the method of reduction of order to find a second solution of the given differential equation. 18. 12y"-4ty' +6y=0, t> 0; 19. 12y" +2ty' - 2y = 0, t> 0; 20. t2y" + 3ty' + y = 0, t> 0; 21. xy" - y' +4x³y = 0, x > 0; y₁(t) = 1² y₁(t) = t y(t) = 1-¹ y₁(x) = sin(x²) 22 ll 11 for an 1-kc the coc nonneg = 0 t as t Thus w
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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