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 goes through the point $(1,0)$.

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

Draw the slope field for the differential equation $\frac{dy}{dx} = xy$ on a grid, then sketch the particular solution passing through $(1,2)$.

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 $\frac{dy}{dx} = -\frac{x}{y}$ and sketch the solution passing through $(1,1)$.

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 a set of axes, construct the slope field for $\frac{dy}{dx} = x^2 - y$ and sketch the particular solution through $(-1,2)$.

On graph paper, draw the slope field for $\frac{dy}{dx} = \frac{y}{x}$ (for $x\neq0$) and sketch the particular solution passing through $(1,2)$.

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

Construct the slope field for $\frac{dy}{dx} = \frac{y-2}{x+1}$ (for $x\neq -1$) and sketch the particular solution through the point $(0,3)$.

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