N/4 less than or equal to 5
Answer:
Step-by-step explanation:
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:
-3.5 or 3 1/2
Step-by-step explanation:

=3
r=common ratio: 12/6=2; 6/3=2
r=2,

=

*3
plug in 12 for n:

=
*3

=

*3

=2048*3

=6144
The twelfth term in the sequence is 6144