MATH3331 Exercise 3 Solutions - UCA
[Pages:1]Math 3331 Exercises
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve.
1.
dy dx
=
x-y x
:
Linear, homogeneous, exact.
2.
dy dx
=
1 y-x
:
Linear in x.
3.
(x
+
1)
dy dx
= -y + 10:
separable, linear,
exact.
4.
dy dx
=
1 x(x-y)
:
Bernoulli in x.
5.
dy dx
=
y2 x2
+y +x
:
separable.
6.
dy dx
=
5y
+
y2:
separable, linear in x, Bernoulli
7. ydx = (y - xy2)dy: linear in x.
8.
x
dy dx
= yex/y - x:
homogeneous
9. xyy + y2 = 2x: Bernoulli.
10. 2xyy + y2 = 2x2: homogeneous, exact, Bernoulli
11. ydx + xdy = 0: linear, exact, separable, homogeneous.
12.
x2
+
2y x
dx = (3 - ln x2)dy: exact, linear in y.
13.
dy dx
=
x y
+
y x
+
1:
homogeneous.
14.
y x2
dy dx
+
e2x2+y2
=
0:
separable.
1
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