IB Mathematics Applications & Interpretation 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 $(1,1)$.

Draw on this

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 $(0,1)$.

Draw on this

On graph paper, draw the slope field for the differential equation $\frac{dy}{dx}=\frac{y}{x}$ for $x\ne 0$ 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 $(1,2)$.

Draw on this

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 $(1,1)$.