Answer:A
Step-by-step explanation:
I got it correct on the test

Look for an integrating factor
:

Multiply both sides by
:

Condense the left side as the derivative of a product:
![\dfrac{\mathrm d}{\mathrm dt}\left[(t+1)^{-7/9}y\right]=\dfrac{14}9t(t+1)^{-16/9}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5B%28t%2B1%29%5E%7B-7%2F9%7Dy%5Cright%5D%3D%5Cdfrac%7B14%7D9t%28t%2B1%29%5E%7B-16%2F9%7D)
Integrate both sides:

For the integral on the right, substitute






Given that
, we get

