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For this equation to be true, A and B and C must satisfy the following system of equations. -2A-B+2C=0 -2B-2C=-2 -2C=4 Solving it yields A= -7/2 and B = 3 and C= -2, which means Up(t)=-/+ 3t-2t². Therefore,

For this equation to be true, A and B and C must satisfy the following system of equations. -2A-B+2C=0 -2B-2C=-2 -2C=4 Solving it yields A= -7/2 and B = 3 and C= -2, which means Up(t)=-/+ 3t-2t². Therefore,

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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Can you show how they solved for 7/2, 3 & 2. (Part i circled)

The particular solution satisfies yp — yp — 2yp = −2t+4t². Since the inhomogeneous term is a polynomial, we assume the solution is of the form Yp(t) = A + Bt + Ct². Substitute this into the ODE to determine A. (A + Bt + Ct²)" − (A + Bt + Ct²)' − 2(A + Bt + Ct²) = −2t + 4t² (B + 2Ct)' — (B + 2Ct) − 2(A + Bt + Ct²) = −2t + 4t² (2C) − (B + 2Ct) — 2(A + Bt + Ct²) = −2t + 4t² 2C - B2Ct – 2A – 2Bt – 2Ct² = −2t + 4t² (-2AB+ 2C) + (-2B2C)t + (-2C)t² = -2t+4t² www.stemjock.com Boyce & DiPrima ODEs 10e: Section 3.5 - Problem 3 For this equation to be true, A and B and C must satisfy the following system of equations. -2A - B + 2C = 0 Therefore, Solving it yields A = −7/2 and B = 3 and C = −2, which means 7 -2B2C = −2 -2C = 4 Yp(t) = 2 + 3t - 2t². y(t) = C₁e-t + C₂e²t 77. 2 Page 2 of 2 + 3t - 2t².
Transcribed Image Text:The particular solution satisfies yp — yp — 2yp = −2t+4t². Since the inhomogeneous term is a polynomial, we assume the solution is of the form Yp(t) = A + Bt + Ct². Substitute this into the ODE to determine A. (A + Bt + Ct²)" − (A + Bt + Ct²)' − 2(A + Bt + Ct²) = −2t + 4t² (B + 2Ct)' — (B + 2Ct) − 2(A + Bt + Ct²) = −2t + 4t² (2C) − (B + 2Ct) — 2(A + Bt + Ct²) = −2t + 4t² 2C - B2Ct – 2A – 2Bt – 2Ct² = −2t + 4t² (-2AB+ 2C) + (-2B2C)t + (-2C)t² = -2t+4t² www.stemjock.com Boyce & DiPrima ODEs 10e: Section 3.5 - Problem 3 For this equation to be true, A and B and C must satisfy the following system of equations. -2A - B + 2C = 0 Therefore, Solving it yields A = −7/2 and B = 3 and C = −2, which means 7 -2B2C = −2 -2C = 4 Yp(t) = 2 + 3t - 2t². y(t) = C₁e-t + C₂e²t 77. 2 Page 2 of 2 + 3t - 2t².
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