1 yy" + (y')? = yy' y(0) = 1, y'(0) = 2

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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Question
Show the complete solution, choices are in the second image.
SOLUTION
a.
y? = e-x
C y?
b.
x2 =
y
= (2x – 3y)^3 (x + y)^2
С.
9 y + 2
C =In |(sec(tan-1 6) +)
d.
У — 1
-1
1
(tan)
- Csc
3(у — 1)
s = [C(x – C,)j
f.
C = x²y² + 4x – 6y
1
C =
3
3
g.
+ y?)7 – xy
2 In |sin |+C
h.
S =
Cos
i.
C = s²t – tet + et
j.
y? = -x²e-*(sin x + cos x) + Cx²
2y? + 6у — 1
c =V16 – x² – 8sin-Ğ) -
k.
4
2y + 3
cos 2y +
sin 2y
4
1-cos y
|
I.
x =
y2
1
m.
= -
x2
sin 4y + (C – 4y)sin?(2y)
x3
y =+ (C – 1)x + (2C, – 1) In |x – 1| + C2
n.
e.
Transcribed Image Text:SOLUTION a. y? = e-x C y? b. x2 = y = (2x – 3y)^3 (x + y)^2 С. 9 y + 2 C =In |(sec(tan-1 6) +) d. У — 1 -1 1 (tan) - Csc 3(у — 1) s = [C(x – C,)j f. C = x²y² + 4x – 6y 1 C = 3 3 g. + y?)7 – xy 2 In |sin |+C h. S = Cos i. C = s²t – tet + et j. y? = -x²e-*(sin x + cos x) + Cx² 2y? + 6у — 1 c =V16 – x² – 8sin-Ğ) - k. 4 2y + 3 cos 2y + sin 2y 4 1-cos y | I. x = y2 1 m. = - x2 sin 4y + (C – 4y)sin?(2y) x3 y =+ (C – 1)x + (2C, – 1) In |x – 1| + C2 n. e.
1
yy" + (y')2 = yy' y(0) = 1, y'(0)
2
Transcribed Image Text:1 yy" + (y')2 = yy' y(0) = 1, y'(0) 2
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