Classify each differential equation. Some equations may be more than one kind. Do not solve. (Select all that apply of the following for each) :
separable
exact
linear in x
linear in y
homogeneous
Bernoulli in x
Bernoulli in y
none of the above
(a)
| dy |
| dx |
=
| x ? y |
| x |
(b)
| dy |
| dx |
=
| 6 |
| y ? x |
(c) (x + 1)
| dy |
| dx |
= ?y + 10
(d)
| dy |
| dx |
=
| 1 |
| x(x ? y2) |
(e)
| dy |
| dx |
=
| y3 + y |
| x3 + x |
(f)
| dy |
| dx |
= 4y + y2
(g)
y dx = (y + xy2) dy
(h) x
| dy |
| dx |
= yexy ? x
(i)
xyy' + y2 = 2x
(j)
2xyy' + y2 = 2x2
(k)
x dx + y dy = 0
(l)
x2 +
| 2y |
| x |
dx = (3 ? ln x2) dy
(m)
| dy |
| dx |
=
| x |
| y |
+
| y |
| x |
+ 1
(n)
| y |
| x2 |
| dy |
| dx |
+ e2x3 + y2 = 0