= - Given that y C₁e + c₂e* is a two-parameter family of solutions of y" - y = 0 on the interval (-∞, ∞), find a member of the family satis- fying the initial conditions y(0) = 0, y'(0) = 1. Find a solution of the differential equation in Problem 1 satisfying the boundary conditions y(0) = 0, y(1) = 1. -X Given that y = c₁e4x + c₂e* is a two-parameter family of solutions of y" - 3y' - 4y = 0 on the interval (-∞, ∞), find a member of the fam- ily satisfying the initial conditions y(0) = 1, y'(0) = 2.
= - Given that y C₁e + c₂e* is a two-parameter family of solutions of y" - y = 0 on the interval (-∞, ∞), find a member of the family satis- fying the initial conditions y(0) = 0, y'(0) = 1. Find a solution of the differential equation in Problem 1 satisfying the boundary conditions y(0) = 0, y(1) = 1. -X Given that y = c₁e4x + c₂e* is a two-parameter family of solutions of y" - 3y' - 4y = 0 on the interval (-∞, ∞), find a member of the fam- ily satisfying the initial conditions y(0) = 1, y'(0) = 2.
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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Transcribed Image Text:4.1.1
Initial-Value and Boundary-Value Problems
=
1. Given that y
C₁e + c₂e is a two-parameter family of solutions of
y" - y = 0 on the interval (-∞, ∞), find a member of the family satis-
fying the initial conditions y(0) = 0, y'(0) = 1.
2. Find a solution of the differential equation in Problem 1 satisfying the
boundary conditions y(0) = 0, y(1) = 1.
3. Given that y
4x
C₁e¹x + c₂ex is a two-parameter family of solutions of
y" - 3y' - 4y = 0 on the interval (-∞, ∞), find a member of the fam-
ily satisfying the initial conditions y(0) = 1, y'(0) = 2.
=
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