Slope fields

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Understanding Slope Fields
Find the directional field for the following equations:
1. $\frac{dy}{dx}=xy-x$
2. $\frac{dy}{dx}=\frac{x^2}{(y+1)}$
Determining the Equation from a Slope Field
Which equation best corresponds to the following slope field?

i.
$\frac{dy}{dx}=y-2$ $\frac{d y}{d x} = y - 2$
ii.
$\frac{dy}{dx}=xy-2$ $\frac{d y}{d x} = x y - 2$
iii.
$\frac{dy}{dx}=x+1$ $\frac{d y}{d x} = x + 1$
iv.
$\frac{dy}{dx}=-x+1$ $\frac{d y}{d x} = - x + 1$
Which equation best corresponds to the following slope field?

i.
$\frac{dy}{dx}=xy-2$ $\frac{d y}{d x} = x y - 2$
ii.
$\frac{dy}{dx}=-\frac{y}{x}$ $\frac{d y}{d x} = - \frac{y}{x}$
iii.
$\frac{dy}{dx}=2x+y$ $\frac{d y}{d x} = 2 x + y$
iv.
$\frac{dy}{dx}=xy-3$ $\frac{d y}{d x} = x y - 3$
Given the differential equation and its resulting slope field:
$\frac{dy}{dx}=\frac{y}{2}(y-3)$ $\frac{d y}{d x} = \frac{y}{2} (y - 3)$

Draw a solution to the following differential equation using the following initial value conditions:
1. $y(-2)=1$
2. $y(0)=4$
3. $y(1)=3$