Consider the initial value problem dy/dx = 2x/(y − 1), y(0) = y0. a. Solve this initial value problem for y0 ∈ R\{1}. Always give as large as possible interval at which the solution exists. b. Describe the set of solutions geometrically and make a sketch of the total pattern of solutions. What happens if y0  → 1? please if able provide some explanation with the steps, thank you in adavance.

Please don't provide handwritten solution...

1. An object is thrown into the air, and t seconds later its height is h = f(t)=-4.9t² +14.7t meters. Fill in the table below, and use your information to estimate the instantaneous velocity of the object at time t = 2. Show your calculations in the space at the bottom and be sure to include units in your final answer! [2,2.1] [2,2.01] [2,2.001] [2,2.0001] Time interval Average velocity The instantaneous velocity at time t = 2 is approximately: