Consider this differential equation for y = y(x): (* ) dy 1+yz 1+ 22' Find the general solution, and use it to complete parts (a)-(c) below. (a) Find the solution y(a) for (*) that satisfies the additional requirement y(0) = 0. Determine the largest open interval containing z = 0 on which the identity (*) is valid. (Use interval notation to enter your answer; type "inf" to represent co.) y(z) = for r E (b) Repeat part (a), but use the modified initial condition y(0) = -9. y(z) = , for r E (c) Repeat part (a), but use the modified initial condition y(0) = 2. y(z) = , for a E Hint: tan(0 + $) = tan(0) + tan($) 1 - tan(0) tan($)