Write the system in the form 1-1 4]+ x' = etx7ty + 4 sin(t) - y = 8 tan(t)y + 4x − 4 cos(t) d ["] = P(0) ["] dt + f(t). help (formulas) help (matrices) Note: Use prime notation for derivatives and write x and x', etc., instead of x(t), x'(t), or da.
Write the system in the form 1-1 4]+ x' = etx7ty + 4 sin(t) - y = 8 tan(t)y + 4x − 4 cos(t) d ["] = P(0) ["] dt + f(t). help (formulas) help (matrices) Note: Use prime notation for derivatives and write x and x', etc., instead of x(t), x'(t), or da.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
8. Ordinary
![**Transcription**
**Task:** Write the system
\[ x' = e^{4t} x - 7ty + 4 \sin(t) \]
\[ y' = 8 \tan(t) y + 4x - 4 \cos(t) \]
in the form
\[
\frac{d}{dt}
\begin{bmatrix}
x \\
y
\end{bmatrix}
=
P(t)
\begin{bmatrix}
x \\
y
\end{bmatrix}
+
\vec{f}(t).
\]
**Matrix Setup:**
\[
\begin{bmatrix}
\text{[ ]} \\
\text{[ ]}
\end{bmatrix}
=
\begin{bmatrix}
\text{[ ]} & \text{[ ]} \\
\text{[ ]} & \text{[ ]}
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
+
\begin{bmatrix}
\text{[ ]} \\
\text{[ ]}
\end{bmatrix}
\]
**Helpful Resources:**
- Help (formulas)
- Help (matrices)
**Note:** Use prime notation for derivatives and write \( x \) and \( x' \), etc., instead of \( x(t) \), \( x'(t) \), or \( \frac{dx}{dt} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2F118f090e-0706-41bd-8075-88665408729c%2Finf1q58_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription**
**Task:** Write the system
\[ x' = e^{4t} x - 7ty + 4 \sin(t) \]
\[ y' = 8 \tan(t) y + 4x - 4 \cos(t) \]
in the form
\[
\frac{d}{dt}
\begin{bmatrix}
x \\
y
\end{bmatrix}
=
P(t)
\begin{bmatrix}
x \\
y
\end{bmatrix}
+
\vec{f}(t).
\]
**Matrix Setup:**
\[
\begin{bmatrix}
\text{[ ]} \\
\text{[ ]}
\end{bmatrix}
=
\begin{bmatrix}
\text{[ ]} & \text{[ ]} \\
\text{[ ]} & \text{[ ]}
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
+
\begin{bmatrix}
\text{[ ]} \\
\text{[ ]}
\end{bmatrix}
\]
**Helpful Resources:**
- Help (formulas)
- Help (matrices)
**Note:** Use prime notation for derivatives and write \( x \) and \( x' \), etc., instead of \( x(t) \), \( x'(t) \), or \( \frac{dx}{dt} \).
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