d'y dt2 dy + 4 + 3y = 20 sin(t) where y(0): -2, (0): - 4. Find the solution to the IVP %3D
d'y dt2 dy + 4 + 3y = 20 sin(t) where y(0): -2, (0): - 4. Find the solution to the IVP %3D
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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![**Find the solution to the IVP**
\[ \frac{d^2y}{dt^2} + 4 \frac{dy}{dt} + 3y = 20 \sin(t) \]
where \( y(0) = -2 \), \[ \frac{dy}{dt} \](0) = -4.
\[ y(t) = \]
---
In the image provided, we have a second-order linear non-homogeneous differential equation with initial conditions. The objective is to find the function \( y(t) \) that satisfies both the differential equation and the given initial conditions. The equation incorporates both the derivatives \( \frac{d^2y}{dt^2} \) and \( \frac{dy}{dt} \), and a forcing function \( 20 \sin(t) \).
The initial conditions provided are \( y(0) = -2 \) and \( \frac{dy}{dt}(0) = -4 \). The box next to \( y(t) = \) is where the solution to the equation should be inputted.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facdec92e-028d-4f37-af60-841922a4cee5%2F7318d525-d5cd-4274-9bb4-75f6d29a12d4%2Fiy0cvyt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the solution to the IVP**
\[ \frac{d^2y}{dt^2} + 4 \frac{dy}{dt} + 3y = 20 \sin(t) \]
where \( y(0) = -2 \), \[ \frac{dy}{dt} \](0) = -4.
\[ y(t) = \]
---
In the image provided, we have a second-order linear non-homogeneous differential equation with initial conditions. The objective is to find the function \( y(t) \) that satisfies both the differential equation and the given initial conditions. The equation incorporates both the derivatives \( \frac{d^2y}{dt^2} \) and \( \frac{dy}{dt} \), and a forcing function \( 20 \sin(t) \).
The initial conditions provided are \( y(0) = -2 \) and \( \frac{dy}{dt}(0) = -4 \). The box next to \( y(t) = \) is where the solution to the equation should be inputted.
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