Ya what the person above me said
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
Answer:
the faster cyclist was going 18 mph
the slower cyclist was going 9 mph
Step-by-step explanation:
72 ÷ 4 = 18
18 ÷ 2 = 9
2.

(this is given in the first sentence)
3.

and

due to ...
7. ... the alternate interior angles theorem (which holds because

and

are parallel)
8. Because the above establishes that

, which means

, which in turn means

is a parallelogram.