Question

Consider the differential equation y' = y2 − 9 . Let f(x, y) = y2 −...

Consider the differential equation
y' =

y2 − 9
.
Let
f(x, y) =

y2 − 9
.
Find the partial derivative of f.
df
dy
=
Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point
(x0, y0)
in the region.
A unique solution exits in the entire x y-plane.
A unique solution exists in the region −3 < y < 3.
A unique solution exits in the regions y < −3, −3 < y < 3, and y > 3.
A unique solution exists in the region y < −3 or y > 3.
A unique solution exits in the region consisting of all points in the x y-plane except (0, 3) and (0, −3).
Determine whether Theorem 1.2.1 guarantees that the differential equation possesses a unique solution through
(4, 3).
Yes
No
Math   Calculus   
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