Question Type 2: Sketching a solution curve that passes through a specific point using a slope field diagram Exercises

On a coordinate plane, construct the slope field for $\frac{dy}{dx} = y - x$. Sketch the solution curve that passes through the point $(1, 0)$.

Construct the slope field for $\frac{dy}{dx} = \sin(x) + y$ and sketch the solution curve that goes through $(\pi,0)$.

Draw the slope field for $\frac{\text{d}y}{\text{d}x} = -\frac{x}{y}$ on the grid provided below and sketch the solution curve passing through the point $(1, 1)$.

On the grid provided in the specification, construct the slope field for the differential equation $\frac{dy}{dx} = \frac{y-2}{x+1}$ at the 20 indicated points where $x \in \{-3, -2, 0, 1\}$ and $y \in \{0, 1, 2, 3, 4\}$.

Hence, sketch the particular solution to the differential equation that passes through the point $(0, 3)$.

Sketch the slope field for $\frac{dy}{dx} = e^{-x}-y$ and draw the solution curve that passes through the point $(0,1)$.

On graph paper, sketch the slope field for the logistic differential equation $\frac{dy}{dx}=y(1-y)$ and draw the particular solution through $(0,0.5)$.

On the coordinate grid below, draw the slope field for the differential equation $\frac{dy}{dx} = x + y$ for $x, y \in [-3, 3]$. Then sketch the particular solution curve passing through the point $(0,1)$.

On graph paper, draw the slope field for the differential equation $\frac{dy}{dx} = \frac{y}{x}$ for $x \neq 0$ and sketch the particular solution passing through the point $(1, 2)$.

On the coordinate grid provided below:

(a) Draw the slope field for the differential equation $\frac{dy}{dx} = xy$.

(b) Sketch the particular solution curve that passes through the point $(1, 2)$.

On a set of axes, construct the slope field for the differential equation $\frac{\text{d}y}{\text{d}x} = x^2 - y$ for the domain $-2 \le x \le 2$ and range $-1 \le y \le 3$, evaluating the slopes at all integer grid points.

Sketch the particular solution that passes through the point $(-1, 2)$.

Draw the slope field for the differential equation $\frac{dy}{dx} = y^2 - x^2$ for $x, y \in \{-1, 0, 1, 2\}$, and sketch the particular solution curve passing through the point $(1,1)$.