In Problems 1-6, determine the largest interval (a, b) for which Theorem 1 guarantees the existence of a unique solu- ti

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In Problems 1 6 Determine The Largest Interval A B For Which Theorem 1 Guarantees The Existence Of A Unique Solu Ti 1 (62.86 KiB) Viewed 25 times

In Problems 1-6, determine the largest interval (a, b) for which Theorem 1 guarantees the existence of a unique solu- tion on (a, b) to the given initial value problem. 1. xy" – 3y' + e'y = x2 - 1 ; y(-2) = 1, y'(-2) = 0, y"(-2) = 2 2. y" – Vxy = sinx; y(TT) = 0, y'(m) = 11, y"(7) = 3 3. y" -y” + Va- ly = tanx ; y y(5) = y'(5) = y"(5) = 1 4. x(x + 1)y" – 3xy' + y = 0; y(-1/2) = 1, y'(-1/2) = y"(-1/2) = 0 5. xx+ ly" - y + xy = 0; y(1/2) = y'(1/2) = -1, y" (1/2) = 1 6. (x2 - 1)y" + e'y = Inx; " y(3/4) = 1, y'(3/4) = y"(3/4) = 0) - -