dy = cos y. y(4) = 1/4 dx 28. 27
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please send handwritten solution for Q 28
Transcribed Image Text:1.4 Problems
Find general solutions (implicit if necessary, explicit if conve-
nient) of the differential equations in Problems 1 through 18.
Primes denote derivatives with respect to x.
dy
dy
1.
+ 2xy = 0
2.
+ 2xy² = 0
dx
dx
dy
dy
3.
= y sin x
4. (1+x)
= 4y
dx
dx
dy
5.
– y?
6.
= 3/xy
dx
dx
dy
7.
3 (64ху)\в
dx
dy
8.
= 2x sec y
dx
9. (1 – x²) = 2y
10. (1+x)²
dx
= (1 + y)?
dx
11. у %3 ху
12. yy' = x(y² + 1)
dy _1+ a
1+ y
dy
13. y = (y* + 1) cos x 14.
%3D
dx
dx
dy
(x – 1)y³
15.
dx
x²(2y³ – y)
16. (x² + 1)(tan y)y' = x
17. y' = 1+x+y+xy (Suggestion: Factor the right-hand
side.)
18. x*y = 1-x²+ y? – x²y?
Find explicit particular solutions of the initial value problems
in Problems 19 through 28.
dy
19.
= ye", y(0) = 2e
dx
dy
20.
= 3x²(y² + 1), y(0) = 1
dx
dy
21. 2y
dx
y(5) = 2
Vx? – 16
dy
22.
= 4x³y – y. y(1) = -3
dx
dy
23.
dx
+1 = 2y, y(1) = 1
dy
24. (tan x)-
- = y. y (7) = }7
dx
dy
25. x-
y = 2x²y, y(1) = 1
dy
26.
= 2xy² + 3x²y², y(1) = -1
dx
dy
27.
= 6e²x-y, y(0) =0
%3D
dx
28. 2
dx
- cos y, y(4) = 1/4
29. (a) Find a general solution of the differential equation
dy/dx = y. (b) Find a singular solution that is not in-
cluded in the general solution. (c) Inspect a sketch of typi-
cal solution curves to determine the points (a, b)for which
the initial value problem y = y', y(a) = b has a unique
solution.
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