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Multiple-Choice Test Chapter 10.01 Introduction to Partial Differential Equations 1.
A partial differential equation requires (A) exactly one independent variable (B) two or more independent variables (C) more than one dependent variable (D) equal number of dependent and independent variables
2.
Using substitution, which of the following equations are solutions to the partial differential equation? 2
∂ u ∂ x
3.
2
2
=
9
∂ u ∂ y
2
(A)
cos(3 x − y )
(B) (C)
x
(D)
e
2
+ y
2
sin(3 x − 3 y ) −3π x
sin(π y )
The partial differential equation 2
5
∂ z ∂ x
2
2
+6
∂ z ∂ y
2
= xy
is classified as (A) elliptic (B) parabolic (C) hyperbolic (D) none of the above 4.
The partial differential equation xy
∂ z ∂ x
2
=
5
∂ z ∂ y
2
is classified as (A) elliptic (B) parabolic (C) hyperbolic (D) none of the above
10.06.1
10.06.2
5.
Chapter 10.06
The partial differential equation 2
∂ z ∂ x
2
2
−5
∂ z ∂ y
2
=
0
is classified as (A) elliptic (B) parabolic (C) hyperbolic (D) none of the above 6.
The following is true for the following partial differential equation used in nonlinear mechanics known as the Korteweg-de Vries equation. ∂w ∂t
(A) (B) (C) (D)
04.06.2
3
+
∂ w ∂ x
3
− 6w rd
∂w ∂ x
=
0
linear; 3 order rd nonlinear; 3 order st linear; 1 order st nonlinear; 1 order
