(b) Consider the initial value problem: ydydx=4xx2-1,y(0)=2i. Rewrite this equation in the form dydx=f(x,y) and clearly identify f(x,y).Tewrite this equation in the form dydx=f(x,y) and clearly identify f(x,y). '??d4=ydy2=4x2-1ax=12y2=(2ln|y2-1)+cii. Determine whether f(x,y) and delfdely are continuous at the given initial point.etermine whether f(x,y) and ydely are con 2(2)2=2ln102-11+C2=2ln(1)+C2=0+CC=2iii. Can you apply the Existence and Uniqueness Theorem to guarantee a uniquesolution to this initial value problem inan interval containing the initial value?If yes, explain why and find the interval of existence for the solution.Ifno, explain why not.Yes You can when you adace the 2You get a postre rout?2ln|x2-1|+12iv. Give two examples ofan initial condition for which this differential equation is notguaranteed to have a unique solution.