if the initial condition is (0, 1), what is the range of the solution curve y = f(x) for x ≥ 0?
if the initial condition is (0, 1), what is the range of the solution curve y = f(x) for x ≥ 0?
Answer
Explanation:
Step1: Analyze the slope - field and initial condition
We start at the point $(0,1)$. By following the direction of the slope - field for $x\geq0$.
Step2: Observe the behavior of the solution curve
As we move along the solution curve starting from $(0,1)$ and for $x\geq0$, we see that the solution curve approaches the horizontal line $y = 2$ from below. The solution curve never goes above $y = 2$ and is always greater than or equal to $1$ (since we start at $y = 1$ and the slopes in the region below $y = 2$ keep the curve from going below $1$ for $x\geq0$).
Answer:
$1\leq y<2$