Question

(1 point) Consider the first order differential equation x' + = 25% = For each of the initial conditions below, determine the largest interval on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution. (Write the interval in the form a < t < b) a. y(-7) = -0.5. help inequalities) b. (-1.5) = -5.5. help (inequalities) C. y(0) = 0. help inequalities) d. y(7.5) = 2.6. help inequalities) e. y(14) = -0.5. help (inequalities)

Answer 1

- Fundamental theorem of existance of unique noss of linean equations . Let y't PCA) y = 4(4), Yto)= yo if both PCA) and act Continious on open interval ak to Lß, then there exista Unique Solution of IVP on ca. ß). o Mone our giren equation (45)C6-25) P(t)- Ep 964) = e then PCA) has dis con tunities ts. and alt) has discontunity at Ag. then (-00,-5), (-5,5), (5,9), (9,0) in those open intoural both PCA) and alt Continious fundamental theorem then aying @ © © Y61) = -0.5 12.0,-5) ] C-18) = -5.5 165,5) y lo co 65,5) 7 y (+5) = 216 5,9) Since - 7 €(000,-5) since -1.566-5,5) Since o € (-5.5) Since tag € (5,9) since 14+ (9.00) (14) -0.6 19.00)