x - Oregon State University

MISCELLANEOUS PROBLEMS
1.
2.
3.
4.
5.
6.
7.
dy
x3 −2y
=
dx
x
dy
1+cos x
dx = 2−sin y
2x+y
dy
=
dx
3+3y 2 −x
dy
dx = 3 − 6x + y −
2xy+y 2 +1
dy
=
−
dx
x2 +2xy
dy
+ xy = 1 − y,
x dx
dy
4x3 +1
=
dx
y(2+3y)
2xy
y(1) = 0
dy
8. x dx
+ 2y =
9.
dy
dx
=
sin x
x
− 2xy+1
x2 +2y
dy
10. (x2 + xy − y) + (x2y − 2x2) dx
=0
dy
11. (x2 + y) + (x + ey ) dx
=0
12.
13.
dy
dx
dy
dx
+y =
1
1+ex
= 1 + 2x + y 2 + 2xy 2
dy
14. (x + y) + (x + 2y) dx
= 0, y(2) = 3
dy
15. (ex + 1) dx
= y − yex
16.
17.
18.
19.
20.
dy
dx
dy
dx
dy
dx
dy
dx
dy
dx
=
e−x cos y−e2y cos x
−e−x sin y+2e2y sin x
= e2x + 3y
+ 2y = e−x
=
2 −2x
3x2 −2y−y 3
2x+3xy 2
= ex+y
, y(0) = 3
21.
22.
23.
dy
dx
2
+6y−4
+ 3x2y2+4xy+3y
2 = 0
dy
x2 −1
, y(−1) =
=
dx
y 2 +1
2t
t dy
dt + (t + 1)y = e
1
dy
24. (2 sin y sin x cos x + cos y sin2 x) dx
=0
25. xy 0 = y + xey/x
26.
dy
dx
=
x
x2 y+y 3
dy
27. (2y + 3x) = −x dx
28.
dy
dx
=
x+y
x−y
dy
=0
29. (3y 2 + 2xy) − (2xy + x2) dx
30.
dy
dx
2
2
3x y+y
= − 2x
3 +3xy
31. xy 0 + y − y 2e2x = 0, y(1) = 2
32. It started snowing at a heavy and steady rate. A snowplow starts
at noon and travels 2 miles the first hour and 1 mile the second hour.
What time did it start snowing?

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