A slope field for dy/dx = -x/y shows slopes that

Are zero on the x-axis (where y\ne 0) and undefined where y=0 — circles centered at origin are solutions Separable: y\,dy = -x\,dx \Rightarrow y^2/2 = -x^2/2 + C → x^2 + y^2 = const. Solutions are concentric circles.

Are zero on the x-axis (where y\ne 0) and undefined where y=0 — circles centered at origin are solutions

Match y = e^x as a particular solution

Slope Fields

AP Calculus AB· difficulty 4/5

dy/dx = -x/y

A
$y\ne 0$
check_circle
B
$Are constant everywhere$
C
$y = e^x$
D
$Form straight horizontal lines$

Explanation

y\,dy = -x\,dx \Rightarrow y^2/2 = -x^2/2 + C

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