Solve the following differential equation ý +y= , y(0) = 0, y (0) = 1 sin sin cos1 + ain 3 sin t y() %3D -21 cost+ sin t %3D 1 O y(t) = 1 1 sin t Cos t -
Solve the following differential equation ý +y= , y(0) = 0, y (0) = 1 sin sin cos1 + ain 3 sin t y() %3D -21 cost+ sin t %3D 1 O y(t) = 1 1 sin t Cos t -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Solve the following differential equation:
\[ y'' + y = e^{2t}, \quad y(0) = 0, \quad y'(0) = 1 \]
Options:
1. \( y(t) = \frac{1}{5} e^{2t} - \frac{1}{5} \cos t - \frac{3}{5} \sin t \)
2. \( y(t) = \frac{1}{5} e^{2t} - \frac{1}{5} \cos t + \frac{1}{5} \sin t \)
3. \( y(t) = \frac{1}{5} e^{2t} - \frac{1}{5} \cos t + \frac{3}{5} \sin t \)
4. \( y(t) = \frac{1}{5} e^{-2t} - \frac{1}{5} \cos t + \frac{3}{5} \sin t \)
5. \( y(t) = \frac{1}{5} e^{2t} + \frac{1}{5} \cos t - \frac{1}{5} \sin t \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F313c41c0-bf91-42cc-904b-430da81366aa%2F20538078-524f-4235-9041-c7181651bb51%2Fnjqkql_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve the following differential equation:
\[ y'' + y = e^{2t}, \quad y(0) = 0, \quad y'(0) = 1 \]
Options:
1. \( y(t) = \frac{1}{5} e^{2t} - \frac{1}{5} \cos t - \frac{3}{5} \sin t \)
2. \( y(t) = \frac{1}{5} e^{2t} - \frac{1}{5} \cos t + \frac{1}{5} \sin t \)
3. \( y(t) = \frac{1}{5} e^{2t} - \frac{1}{5} \cos t + \frac{3}{5} \sin t \)
4. \( y(t) = \frac{1}{5} e^{-2t} - \frac{1}{5} \cos t + \frac{3}{5} \sin t \)
5. \( y(t) = \frac{1}{5} e^{2t} + \frac{1}{5} \cos t - \frac{1}{5} \sin t \)
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