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CAAM 336
·
DIFFERENTIAL EQUATIONS
Problem Set 1
Posted Wednesday 25 August 2010. Due Wednesday 1 September 2010, 5pm.
1. [18 points]
For each of the following equations, specify whether each is (a) an ODE or a PDE; (b) determine its
order; (c) specify whether it is linear or nonlinear. For those that are linear, specify whether they are
(d) homogeneous or inhomogeneous, and (e) whether they have constant or variable coeﬃcients.
(1.1)
dv
dx
+
2
x
v
= 0
(1.2)
∂v
∂t

3
∂v
∂x
=
x

t
(1.3)
∂u
∂t

∂
∂x
±
2
u
∂u
∂x
²
= 0
(1.4)
∂u
∂t
+
u
∂u
∂x
+
∂
3
u
∂x
3
= 0
(1.5)
d
2
y
dx
2

μ
(1

y
2
)
dy
dx
+
y
= 0
(1.6)
d
2
dx
2
±
ρ
(
x
)
d
2
u
dx
2
²
= sin(
x
)
2. [18 points]
Determine whether each of the following functions is a solution of the corresponding diﬀerential equation
from question 1.
(a) Is
v
(
x
) = 1
/x
2
a solution of (1.1) ?
(b) Is
v
(
x,t
) =
t
(
t
+
x
) a solution of (1.2) ?
(c) Is
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 Fall '09
 Tompson

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