3. Solve the following differential equations a) y" -y - 2y = 4t² + 2t
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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Transcribed Image Text:### Differential Equations Problems
Solve the following differential equations:
a) \( y'' - y' - 2y = 4t^2 + 2t \)
b) \( y'' + 7y' + 12y = p \cdot t^2 - 7p \cdot t \)
Initial conditions:
- \( y(0) = 1 \)
- \( \frac{dy}{dt}(0) = 0 \)
c) \( 2y'' + 3y' + 4y = t^2 + 3\sin(t) \)
Initial condition:
- \( y(0) = 1 \)
These equations include second-order derivatives, represented as \( y'' \), and first-order derivatives, represented as \( y' \). Each equation presents a unique challenge with different terms and initial conditions to consider.
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