Consider the differential equation = -1+ dx - dy 2y3 – y2 – 2xy (a) Show that x2 dy (b) Let y = g(x) be the particular s

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Consider The Differential Equation 1 Dx Dy 2y3 Y2 2xy A Show That X2 Dy B Let Y G X Be The Particular S 1 (241.5 KiB) Viewed 36 times

Consider the differential equation = -1+ dx - dy 2y3 – y2 – 2xy (a) Show that x2 dy (b) Let y = g(x) be the particular solution to the differential equation dx y2 -1 + with initial condition x g(4) = 2. Does g have a relative minimum, a relative maximum, or neither at x = 4 ? Justify your answer. dy (c) Let y = h(x) be the particular solution to the differential equation dx 12 with initial condition x = =- h(1) = 2. Write the second-degree Taylor polynomial for h about x = 1. = (d) For the function h given in part (c), it is known that|h''(x) = 60 for all x in the interval 0.9 5x 5 1.1. Let A represent the approximation of h(1.1) found by using the second-degree Taylor polynomial for h about x = 1 from part (c). Use the Lagrange error bound to show that A differs from h(1.1) by at most 0.01