Please disregard my work, I cant figure this problem out and id appreciate help with all 3 questions, work on paper would be best. Thank you F4- I can apply the existence and uniqueness theorems to determine the largestinterval on which a first or second order linear DEis guaranteed to exist, andunderstand what it means for the theorems to not apply.Answer the following questions using the existence and uniqueness theorems.(a) Consider the differential equation(t+3)dydt+t+7t(t-2)(t+8)y=e2t-1.,i5(0,-8)-,-8y(-5)=-5?What about ifwe start with y(-10)=-2?(b) Consider the differential equationdydt=y2+7t+14t+3yWhen eitter oftheselatwes equalWhat dowe know about the interval of existence of the solution to this equation with y(-5)=-6? Here ; 3aWhat about ifwe start with y(3)=-4?(c) Let f(t,y)be a function so that both f and delfdely are continuous for all real numbers t and y. Let thefunction y(t)be the solution to the initial value problemdydt=f(t,y)(y2+8y+15),y(0)=-4Isit possible for the graph ofy(t)to cross the line y=-6?Ifitis possible, must the solution y(t)cross that line? Ifitis possible, give any information you have about the t value where it crosses.In either case, carefully justify your conclusions using results discussed in class. Yes, itis possible for y(t)to cross the line 4=-6,it must cross y=-6becuse itgoes on forever as thefincton is contimo enfor all real numbers.t=-1 when y=-6