3x #3 x dy + (3x-1) y = C-³² dx Step 1: Standard Form dy + dx (3x-1) 4 x Step 2: M(x)= e P(x) = (3x-1) М(x) = е SP(x) SP(X) e e 3-1 = √³-1 = 35- £ - 3 - 1n/x1 + 3 /a/x-²) x 3-In 1x¹1 x -3x X

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I am stuck on the integrating factor of this differential equation. The exponent rules are making me stuck.
#3 x dy + (3x-1) y = e-3x
dx
Step 1: Standard Form
dy +
dx
(3x - 1) y
x
Step 2: M(x)= e
P(x) = (3x-1)
M(x) = е
SP(x)
SP(X)
2
53-4-5-4-
3-
e
35-£-3-1^/x1 =3 /a/x-1)
e-³x
x
3-In 1x²1
Transcribed Image Text:#3 x dy + (3x-1) y = e-3x dx Step 1: Standard Form dy + dx (3x - 1) y x Step 2: M(x)= e P(x) = (3x-1) M(x) = е SP(x) SP(X) 2 53-4-5-4- 3- e 35-£-3-1^/x1 =3 /a/x-1) e-³x x 3-In 1x²1
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