dy dx 3. e3x+2y gotni bys 5. (4y + yx2)dy - (2x + xy²) dx = 0 =

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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Can someone please help me solve these problems I’m having a hard time . Problems 13,15,17,19,21,23
In Problems 1-40 solve the given differential equation by separation of
variables.
dy
dx
1.
3. dx + e³x dy = 0
dy
dx
5. (x + 1)
7. xy' = 4y
dy
y³
dx
2
11.
13.
= sin 5x
2,2
dx mex²y² nom
1 + x
e3x+2y
15. (4y + yx²) dy - (2x + xy²) dx = 0
16. (1 + x² + y² + x²y²) dy = y² dx
dy
dy
dx
21.
23.
-
ds
dr
dP
dt
=
17. 2y(x + 1)dy = x dx
(y + 1²
X
19. y lnx
=
dx
dy
=kS
= x + 6
=
arls
= P - P2
to suley
odsu
2.
3 đối
maldong 8.
4. dx - x²dy = 0
dy
dx
6. ex.
10.
dy
dx
20.
22.
dy
dx
24.
dy
dx
dx
12. =
dy
-= (x + 1)²
dy
dx
dy
14. e'y = ey + e-2x-y
dx
dQ
dt
+ 2xy = 0
=
18. x²y²dy = (y + 1) dx
2y + 3)²
4x + 5,
dN
dt
= 2x
y + 1
X
1 + 2y²
y sin x
=
- k(Q - 70)
+ N = Nte¹+2
Transcribed Image Text:In Problems 1-40 solve the given differential equation by separation of variables. dy dx 1. 3. dx + e³x dy = 0 dy dx 5. (x + 1) 7. xy' = 4y dy y³ dx 2 11. 13. = sin 5x 2,2 dx mex²y² nom 1 + x e3x+2y 15. (4y + yx²) dy - (2x + xy²) dx = 0 16. (1 + x² + y² + x²y²) dy = y² dx dy dy dx 21. 23. - ds dr dP dt = 17. 2y(x + 1)dy = x dx (y + 1² X 19. y lnx = dx dy =kS = x + 6 = arls = P - P2 to suley odsu 2. 3 đối maldong 8. 4. dx - x²dy = 0 dy dx 6. ex. 10. dy dx 20. 22. dy dx 24. dy dx dx 12. = dy -= (x + 1)² dy dx dy 14. e'y = ey + e-2x-y dx dQ dt + 2xy = 0 = 18. x²y²dy = (y + 1) dx 2y + 3)² 4x + 5, dN dt = 2x y + 1 X 1 + 2y² y sin x = - k(Q - 70) + N = Nte¹+2
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