Differential Equations Quiz
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SYSTEMS OF DIFFERENTIAL EQUATIONS
Question 1
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Consider the system of differential equations:
d
x
d
t
=
3
x
−
2
y
+
t
\frac{dx}{dt} = 3x - 2y + t
d
t
d
x
=
3
x
−
2
y
+
t
,
d
y
d
t
=
x
+
4
y
−
e
t
\frac{dy}{dt} = x + 4y - e^t
d
t
d
y
=
x
+
4
y
−
e
t
. Which matrix form correctly represents this system?
A
d
d
t
(
x
y
)
=
(
3
−
2
1
4
)
(
x
y
)
+
(
t
−
e
t
)
\frac{d}{dt}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 3 & -2 \\ 1 & 4 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t \\ -e^t \end{pmatrix}
d
t
d
(
x
y
)
=
(
3
1
−
2
4
)
(
x
y
)
+
(
t
−
e
t
)
B
d
d
t
(
x
y
)
=
(
3
2
1
4
)
(
x
y
)
+
(
t
−
e
t
)
\frac{d}{dt}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t \\ -e^t \end{pmatrix}
d
t
d
(
x
y
)
=
(
3
1
2
4
)
(
x
y
)
+
(
t
−
e
t
)
C
d
d
t
(
x
y
)
=
(
3
−
2
1
4
)
(
x
y
)
+
(
t
e
t
)
\frac{d}{dt}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 3 & -2 \\ 1 & 4 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t \\ e^t \end{pmatrix}
d
t
d
(
x
y
)
=
(
3
1
−
2
4
)
(
x
y
)
+
(
t
e
t
)
D
d
d
t
(
x
y
)
=
(
3
−
2
−
1
4
)
(
x
y
)
+
(
t
−
e
t
)
\frac{d}{dt}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 3 & -2 \\ -1 & 4 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t \\ -e^t \end{pmatrix}
d
t
d
(
x
y
)
=
(
3
−
1
−
2
4
)
(
x
y
)
+
(
t
−
e
t
)
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