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Return to Foundations of Science Mathematics 2e Student Resources
Chapter 13 Multiple choice questions
Ordinary differential equations
Quiz Content
*
not completed
.
Which of the following differential equations is
not
linear?
d
y
/d
x
–
y
^{2}
= 0
correct
incorrect
d
y
/d
x
+ sin(
x
)
y
= 0
correct
incorrect
d
^{2}
y
/d
x
^{2}
+ 3 d
y
/d
x
+ 2
y
= 0
correct
incorrect
x
^{2}
d
^{2}
y
/d
x
^{2}
+
x
d
y
/d
x
–
y
= 0
correct
incorrect
*
not completed
.
Which of the following is
not
true about linear differential equations?
A solution multiplied by a constant is also a solution.
correct
incorrect
The sum of solutions is also a solution.
correct
incorrect
A small change in the boundary conditions can lead to drastically different behaviour of the solutions.
correct
incorrect
The solutions do not display chaotic behaviour.
correct
incorrect
*
not completed
.
What is the integrating factor for
x
d
y
/d
x
–
y
=
x
^{2}
?
e
^{-}
^{x}
correct
incorrect
x
^{-1}
correct
incorrect
x
^{-2}
correct
incorrect
x
^{3}
/ 3
correct
incorrect
*
not completed
.
How would you describe the solution of d
^{2}
y
/d
x
^{2}
+ 2 d
y
/d
x
+ 3
y
= 0 ?
Decaying oscillation.
correct
incorrect
Critically damped oscillation.
correct
incorrect
Sum of decaying solutions (no oscillations).
correct
incorrect
None of the above.
correct
incorrect
*
not completed
.
For the second-order differential equation obeyed by a driven damped harmonic oscillator, which of the following is not related to the other three.
The complementary function.
correct
incorrect
The particular integral.
correct
incorrect
The steady-state solution.
correct
incorrect
The long-term behaviour.
correct
incorrect
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