Solution Found!
Answer: In each of 1 through 4, draw a direction field for the given differential
Chapter 1, Problem 1(choose chapter or problem)
In each of Problem, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as \(t \rightarrow \infty\). If this behavior depends on the initial value of y at \(t=0\), describe the dependency.
\(y^{\prime}=3-2 y\)
Questions & Answers
QUESTION:
In each of Problem, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as \(t \rightarrow \infty\). If this behavior depends on the initial value of y at \(t=0\), describe the dependency.
\(y^{\prime}=3-2 y\)
ANSWER:Step 1 of 4
The given differential equation is.
y' = 3 – 2y
dy/dt = 3-2y
In order to draw the direction field for a given differential equation, we will find the value of dy/dt at different points, i.e., for the different values of y.
Step 2 of 4
\(\begin{array}{c|c|c|c|c|c} \hline \mathrm{y} & 0 & 1 & 3 / 2 & 2 & 3 \\ \hline \mathrm{dy} / \mathrm{dt} & 3