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Read eq.(7) to (11) on page 173, 174 and Theorem 4.8.1 on page 175. Then use Green's function, i.e. eq.(10) to solve IVP Sy" – 5y + 6y = 2e' ly(0) = 0, y'(0) = 0

Read eq.(7) to (11) on page 173, 174 and Theorem 4.8.1 on page 175. Then use Green's function, i.e. eq.(10) to solve IVP Sy" – 5y + 6y = 2e' ly(0) = 0, y'(0) = 0

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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(c) Green's function by yourself. Read eq. (7) to (11) on page 173, 174 and Theorem 4.8.1 on page 175. Then use Green's function, i.e. eq.(10) to solve IVP You are now in front of the door and one step close to derive the famous Jy" – 5y' + 6y = 2e ly(0) = 0, y'(0) = 0 Yp(x) = u1 (x)y1 (æ) + u2 (x)y2 (x). (7) Y2 (æ) f(x) Y1 (x) f(x) u (x) = u (x) = (8) W W p(x) = y1 (2x) / pe -Y2 (t) f(t) y1 (t) f(t) dt (2) : dt + y2 (x) W(t) W (t) (9) -Y1 (x)y2 (t) W(t) Y1 (t)y2 (x) - f(t) dt, W (t) - f(t) dt + »(#) = / G(x,t)f(t) dt. (10) Y1 (t)y2 (x) – y1 (x)y2 (t) W (t) - G(x, t) (11)
Transcribed Image Text:(c) Green's function by yourself. Read eq. (7) to (11) on page 173, 174 and Theorem 4.8.1 on page 175. Then use Green's function, i.e. eq.(10) to solve IVP You are now in front of the door and one step close to derive the famous Jy" – 5y' + 6y = 2e ly(0) = 0, y'(0) = 0 Yp(x) = u1 (x)y1 (æ) + u2 (x)y2 (x). (7) Y2 (æ) f(x) Y1 (x) f(x) u (x) = u (x) = (8) W W p(x) = y1 (2x) / pe -Y2 (t) f(t) y1 (t) f(t) dt (2) : dt + y2 (x) W(t) W (t) (9) -Y1 (x)y2 (t) W(t) Y1 (t)y2 (x) - f(t) dt, W (t) - f(t) dt + »(#) = / G(x,t)f(t) dt. (10) Y1 (t)y2 (x) – y1 (x)y2 (t) W (t) - G(x, t) (11)
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