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Consider the initial-value problem y" + 4y = g(x) where y(0) = 1, y'(0) = 2 Jsinr 0 π/2 (a) Find a solution y₁(z) to the differential equation over the interval 0 π/2. y(x) = (c) The goal is to combine the two solutions 3₁ and 32 into one solution [yi(r) 0T/2 To ensure that y(r) meets the requirements to be a solution to a differential equation, it must be continuous and differentiable. Determine the values of the unknown constants in 32 that ensure y is continuous and differentiable.

Consider the initial-value problem y" + 4y = g(x) where y(0) = 1, y'(0) = 2 Jsinr 0 π/2 (a) Find a solution y₁(z) to the differential equation over the interval 0 π/2. y(x) = (c) The goal is to combine the two solutions 3₁ and 32 into one solution [yi(r) 0T/2 To ensure that y(r) meets the requirements to be a solution to a differential equation, it must be continuous and differentiable. Determine the values of the unknown constants in 32 that ensure y is continuous and differentiable.

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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Consider the initial-value problem y" + 4y = g(x) where g(x) = sina 0≤ ≤/2 I> π/2 10 (a) Find a solution y₁(z) to the differential equation over the interval 0<x</2. Use the initial conditions to determine the unknown constants c₁ and c2. y(0) = 1, y/(0) = 2 (b) Find a solution 72(z) to the differential equation over the interval r> /2. (c) The goal is to combine the two solutions ₁ and 2 into one solution Syn(z) 0<x</2 3₂(T) I>T/2 y(x) = To ensure that y(z) meets the requirements to be a solution to a differential equation, it must be continuous and differentiable. Determine the values of the unknown constants in y2 that ensure y is continuous and differentiable.
Transcribed Image Text:Consider the initial-value problem y" + 4y = g(x) where g(x) = sina 0≤ ≤/2 I> π/2 10 (a) Find a solution y₁(z) to the differential equation over the interval 0<x</2. Use the initial conditions to determine the unknown constants c₁ and c2. y(0) = 1, y/(0) = 2 (b) Find a solution 72(z) to the differential equation over the interval r> /2. (c) The goal is to combine the two solutions ₁ and 2 into one solution Syn(z) 0<x</2 3₂(T) I>T/2 y(x) = To ensure that y(z) meets the requirements to be a solution to a differential equation, it must be continuous and differentiable. Determine the values of the unknown constants in y2 that ensure y is continuous and differentiable.
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