Differential Equations proficient (only). This is the second time I am submitting this question after 6 house wait.

I am happy to rate every answer based on the conditions below.

1. Consider the following differential equation: dy 1- t dt y2 - 4 Perform the following: a) Find the general solution b) Find the particular solution with the initial condition y(0) = -1. Sketch your solution on the slope field obtain from a graphing tool (for ex- ample https: //homepages . bluffton. edu/=nesterd/apps/slopefields. html c) Explain in your own words theorems about existence and uniqueness of solutions of differential equations y' = f(x,y) (Theorem 1 and Theorem 2 from Section 1.3 of the lecture). Use the example from this question to illustrate your thinking. d) In your own words, compare the actual intervals of existence and uniqueness to the conclusions of the theorems