Solve the following initial value problem: =-2y+ 6 y (0) = 7 %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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![### Differential Equations: Initial Value Problem
Solve the following initial value problem:
\[
\begin{cases}
\frac{dy}{dt} = -2y + 6 \\
y(0) = 7
\end{cases}
\]
\[ y(t) = \; \_\_\_\_\_ \quad \]
This initial value problem involves a first-order linear differential equation. The given equation is in the form \(\frac{dy}{dt} = -2y + 6\) with the initial condition \(y(0) = 7\). The goal is to find a function \(y(t)\) that satisfies both the differential equation and the initial condition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73fb2883-df73-4e37-b7ef-66d24e1d1095%2F937764c1-64e3-421d-906d-2b06cfbb2690%2Femo12vm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Differential Equations: Initial Value Problem
Solve the following initial value problem:
\[
\begin{cases}
\frac{dy}{dt} = -2y + 6 \\
y(0) = 7
\end{cases}
\]
\[ y(t) = \; \_\_\_\_\_ \quad \]
This initial value problem involves a first-order linear differential equation. The given equation is in the form \(\frac{dy}{dt} = -2y + 6\) with the initial condition \(y(0) = 7\). The goal is to find a function \(y(t)\) that satisfies both the differential equation and the initial condition.
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