Math 2552 - Differential Equations
Sections F1 – F4; L1 – L4
Georgia Institute of Technology, Fall 2015
Exam 1 Review Problems
Solve the ODEs below. If they are IVPs, give the largest interval where your solution is valid.
1. ydy
dx = (x+xy2)ex2.
2. x2+2y
xdx = (3 −ln x2)dy.
3. dy
dx =x
y+y
x+ 1.
4. 2xyy0+y2= 2x2.
5. y
x2
dy
dx +e2x3+y2= 0.
6. xyy0+y2= 2x.
7. y dx +x dy = 0.
8. dy
dx =1
y−x.
9. ex+ydy −dx = 0.
10. (x2
−1) dy
dx + 2y= (x+ 1)2.
11. dy
dx =y−x
y+x.
12. x dy =yln y dx;y(2) = e.
13. 1 + ln x+y
xdx = (1 −ln x)dy.
14. xy0+y=ex;y(1) = 2.
15. dy −sin x(y+ 2) dx = 0; y(π/2) = 1.
16. dy
dx =xy + 3x−y−3
xy −2x+ 4y−8.
17. yln y
x+ 1dx −x dy = 0.
18. dy
dx =2 ln x
xy
19. dy
dx +1
xy=25x2ln x
2y.
20. dy
dx +2e2x
1 + e2xy=1
e2x−1.
21. dy
dx =sin y+ycos x+ 1
1−xcos y−sin x.
22. (ln(xy) + 1) dx +x
y+ 2ydy = 0.
23. dy
dx −x2y=√yx2.
24. 2x(ln x)y0
−y=−9x3y3ln x.
25. e2x+ydy −ex−ydx = 0.
26. y0+ysin x= sin x.
27. y0+y(tan x+ysin x) = 0.
28. dy
dx =x2
x2−y2+y
x.
29. (3x2+ 2xy2)dx + (2x2y)dy = 0.
30. xy0
−2y= 2x2ln x.
31. (y2+ 3xy +x2)dx −x2dy = 0.
32. y0
−x−1y=x−1px2−y2;x > 0.
33. (1 + x)y0=y(2 + x).
34. (y−ex)dx +dy = 0.
