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5.1 Problems In Problems 1 through 16, a homogeneous second-order lin- ear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 1. y" – y = 0; yı = e*, y2 = e¬*; y(0) = 0, y'(0) = 5 -Зх. 2. у" — 9у — 0%;B у1 — езх, , У2 %3е З*; у(0) — —1, у' (0) — 15 У (0) — — 1, у' (0) — 15 = e

5.1 Problems In Problems 1 through 16, a homogeneous second-order lin- ear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 1. y" – y = 0; yı = e*, y2 = e¬*; y(0) = 0, y'(0) = 5 -Зх. 2. у" — 9у — 0%;B у1 — езх, , У2 %3е З*; у(0) — —1, у' (0) — 15 У (0) — — 1, у' (0) — 15 = e

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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Diff. EQ. 

Second order Diff. Eqns.

Please answer number 2, thank you!

5.1 Problems In Problems 1 through 16, a homogeneous second-order lin- ear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that yı and y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 1. y" – y = 0; yı = e*, y2 = e-*; y(0) = 0, y' (0) = 5 2. у" — 9у 3D 0; У1 3 езх, у2 —е 3*; у(0) 3 —1, у' (0) — 15 Y2 =e-3x. ;y(0) = -1, y'(0) = 15
Transcribed Image Text:5.1 Problems In Problems 1 through 16, a homogeneous second-order lin- ear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that yı and y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 1. y" – y = 0; yı = e*, y2 = e-*; y(0) = 0, y' (0) = 5 2. у" — 9у 3D 0; У1 3 езх, у2 —е 3*; у(0) 3 —1, у' (0) — 15 Y2 =e-3x. ;y(0) = -1, y'(0) = 15
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