Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique solution on (a,b) to the initial value problem below. (-) x(x + 3)у"" - 8ху' + у%3D0, у| - = 1, y' = 0, y'" = 0 ......

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Q: Find the unique solution of the second-order initial value problem. y" + y' - 6y = 0, y(0) = 5,…

A: y''+y'-6y=0(D2+D-6)y=0D2+D-6=0D2+3D-2D-6=0D(D+3)-2(D+3)=0(D-2)(D+3)=0hence the roots areD=2,-3