In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. 9. (2x - y) + (2y - x) y' = 0, y(1) = 3 10. (9x² + y - 1) - (4y - x) y' = 0, y(1) = 0
In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. 9. (2x - y) + (2y - x) y' = 0, y(1) = 3 10. (9x² + y - 1) - (4y - x) y' = 0, y(1) = 0
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
10
Transcribed Image Text:1. (2x+3)+(2y = 2) y' = 0
2. (2x+4y) + (2x - 2y) y' = 0
3. (3x² - 2xy + 2) + (6y² - x² + 3) y' = 0
dy
ax + by
4.
dx
bx + cy
ax - by
bx - cy
5.
6.
7.
8.
dy
dx
(yety cos(2x) -2exy sin(2x)+2x)+(xexy cos(2x)-3) y' = 0
(y/x+6x) + (lnx - 2) y' = 0, x > 0
X
y dy
(x² + y2)3/2 + (x² + y2)3/2 dx = 0
In each of Problems 9 and 10, solve the given initial value problem
and determine at least approximately where the solution is valid.
gnitate noltu
9. (2x - y) + (2y - x) y' = 0,
y(1) = 3
10. (9x² +y-1) - (4y - x) y' = 0, y(1) = 0
In each of Problems 11 and 12, find the value of b for which the given
equation is exact, and then solve it using that value of b.
11. (xy2 + bx2y) + (x + y)x²y' =0
12. (ye2xy + x) + bxe²xy y' = 0
13. Assume that equation (6) meets the requirements of Theorem
2.6.1 in a rectangle R and is therefore exact. Show that a possible
function(x, y) is
= ["MO
where (xo, yo) is a point in R.
(x, y) =
M(s, yo) ds +
[N
N(x, t) dt,
is also exact
In each of E
exact but b
factor. Ther
15. x²y³
16. (x+
17. Show
only, then t
has an integ
In each of F
the given e
18. (3x2-
19. y'=
20. 1+C
21. y+C
22. Solve
using the in
the solution
integrating
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