ax y' + y = sin x; y = sin X - - cos x + 10e-*

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Can you help me I need solving problems 17,19 ,and 21 please
In Problems 11-40 verify that the indicated function is a solution of the given
differential equation. Where appropriate, c₁ and c₂ denote constants.
(11. 2y' + y = 0; y = e-x/2
12. y' + 4y = 32; y = 8
dy
13.
dx
14.
dy
dt
15. y'
16.
-
- 2y = e³x; y = e³x + 10e²x
+ 20y = 24; y = -e-20
=
25+ y²; y = 5 tan 5x
dy y
dx
=
y =(√x + ₁)², x > 0, q > 0
17. y' + y = sin x; y = sin x -
18. 2xy dx + (x² + 2y) dy = 0;
ylimsi
cos x + 10e-*
x²y + y² = ₁
1
19. x² dy + 2xy dx = 0; y = x2
20. (y')³ + xy' = y; y = x + 1
21. y = 2xy' + y(y')²; y² = c₁(x + 1/ cq₁)
Transcribed Image Text:In Problems 11-40 verify that the indicated function is a solution of the given differential equation. Where appropriate, c₁ and c₂ denote constants. (11. 2y' + y = 0; y = e-x/2 12. y' + 4y = 32; y = 8 dy 13. dx 14. dy dt 15. y' 16. - - 2y = e³x; y = e³x + 10e²x + 20y = 24; y = -e-20 = 25+ y²; y = 5 tan 5x dy y dx = y =(√x + ₁)², x > 0, q > 0 17. y' + y = sin x; y = sin x - 18. 2xy dx + (x² + 2y) dy = 0; ylimsi cos x + 10e-* x²y + y² = ₁ 1 19. x² dy + 2xy dx = 0; y = x2 20. (y')³ + xy' = y; y = x + 1 21. y = 2xy' + y(y')²; y² = c₁(x + 1/ cq₁)
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