2(150–x2) 100+r 3x2 100- dt 300–2x2 100+1 3x2 100- dx2 di dx2 (5) (300–2x2)(100–1)–3x½(100+1) %3D dt (100+1)(100–1) 300+1 (100+1)(100–1)*2 = 300 100+r dt Consider the integrating factor for equation (5). 500+ IF =el (100+(100-0 IF = e2 In(t+100)–3 In(t–100) (*+ 100)2 In IF = e" -100) (1+100)? (1-100) IF =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I have a question regarding this answer, specifically at the moment it's solved the IF at step 4, because instead of doing e^∫ 300+t/(100-t)(100+t)dt, 300+t it's changed for 500+t and with that he continues the resolution of the problem.

It's correct or I'm missing something? Thanks

Consider equations (2) and (3).
2(150-x2)
3x2
100-1
dx2
di
100+t
dx2
300–2x2
3x2
dt
100+1
100-1
(5)
(300–2x2)(100-1)-32(100+1)
(100+1)(100-1)
dt
300+t
(100+1)(100–1)
300
X2 D
100+1
dt
Consider the integrating factor for equation (5).
500+
-di
IF =el (100+(100-)
IF
e2 In(t+100)–3 In(1–100)
(+100)2
In
IF = e
(-100)3
(1+100)²
IF =
(1-100)
+
Transcribed Image Text:Consider equations (2) and (3). 2(150-x2) 3x2 100-1 dx2 di 100+t dx2 300–2x2 3x2 dt 100+1 100-1 (5) (300–2x2)(100-1)-32(100+1) (100+1)(100-1) dt 300+t (100+1)(100–1) 300 X2 D 100+1 dt Consider the integrating factor for equation (5). 500+ -di IF =el (100+(100-) IF e2 In(t+100)–3 In(1–100) (+100)2 In IF = e (-100)3 (1+100)² IF = (1-100) +
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