The first y equals -3 and the second y equals -9
Answer: d. He multiplied when he was supposed to divide
Step-by-step explanation:
He just multiplied across when he was supposed to divide (or cross multiply) to find the unit rate :)
The polynomial remainder theorem states that the remainder of the division of a polynomial 
by 
is equal to 
.
Therefore
Multiply the original DE by xy:
xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)
Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes
x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0
This final equation is easily recognized as separable:
dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides
The answer is C.
x=2
y=-30
(2;-30)
