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:
3 1/2 hours.
Step-by-step explanation:
If the Half Time show is one-seventh of the show and lasts for 30 minutes, we can multiply that by 7 to get the total amount of minutes.
30 x 7 = 210
To convert the number of minutes to hours, 210 can be divided by 60 to result in a total of 3.5, therefore, the Super Bowl lasts for 3 1/2 hours.
