Find the solution to the differential equation dydty22t if y

Find the solution to the differential equation dy/dt=y^2(2+t), if y=7 when t=1

y=?

integral dy/y² = integral (2+t)dt

- 1/y = 2t + t²/2 +C, C= integration constant

at y = 7, t = 1

-1/7 = 2.1 + 1²/2 + C

C = -37/14

- 1/y = 2t + t²/2 - 37/14

or y = - 1 / (2t + t2/2 - 37/14)