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Exercises. Find the general solution given one of the homogeneOus solutions. If an initial value is given, solve the IVP. (1) " + ry- y = n =

Exercises. Find the general solution given one of the homogeneOus solutions. If an initial value is given, solve the IVP. (1) " + ry- y = n =

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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Exercises. Find the general solution given one of the homogeneous solutions. If an initial value is given, solve the IVP. 4 (1) /" + ry- = 2i = (2) a" - ry' +y = ; 1 = a (3) " + 4xy + (4a2 + 2) = 8e-(w+2); =- (4) a?" + 2.r(a* - 1)y + (a- 2r + 2)y = a2; n = æe" %3D 3 (5) " + 2ry - 2y = :(1) =(1) =; = = (6) (3r – 1)," - (3r +2)/- (6e-8)y = 0; y (0) = 2, y (0) = 3; y = e %3D (7) y" + 21y - 2y = 0; = (8) 4ay" + 2y' + y = 0; 1 = sin Va (9) (2 - 2r)y" + (2- )/+ (2- 2)u = 0; y1 = e" (10) 4a (sin r)y" - 4a(r cos a + sin e)W+ (2r cos r+3 sin æ)y = 0; y1 = (11) y" + 3ty+y = 0; =-1 (12) (* - 1)y" - ay'+y 0; y1 e"
Transcribed Image Text:Exercises. Find the general solution given one of the homogeneous solutions. If an initial value is given, solve the IVP. 4 (1) /" + ry- = 2i = (2) a" - ry' +y = ; 1 = a (3) " + 4xy + (4a2 + 2) = 8e-(w+2); =- (4) a?" + 2.r(a* - 1)y + (a- 2r + 2)y = a2; n = æe" %3D 3 (5) " + 2ry - 2y = :(1) =(1) =; = = (6) (3r – 1)," - (3r +2)/- (6e-8)y = 0; y (0) = 2, y (0) = 3; y = e %3D (7) y" + 21y - 2y = 0; = (8) 4ay" + 2y' + y = 0; 1 = sin Va (9) (2 - 2r)y" + (2- )/+ (2- 2)u = 0; y1 = e" (10) 4a (sin r)y" - 4a(r cos a + sin e)W+ (2r cos r+3 sin æ)y = 0; y1 = (11) y" + 3ty+y = 0; =-1 (12) (* - 1)y" - ay'+y 0; y1 e"
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