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Consider the differential equation differential equation with the initial condition f(-1) = 2. = 6x²-x²y. Let y = f(x) be a particular solution to this

Consider the differential equation differential equation with the initial condition f(-1) = 2. = 6x²-x²y. Let y = f(x) be a particular solution to this

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Free Response -BC (No Calculator) Consider the differential equation = 6x²-x²y. Let y = f(x) be a particular solution to this dx differential equation with the initial condition f(-1) = 2. (a) Use Euler's method with two steps of equal size, starting at x = -1, to approximate f(0). Show the work that leads to your answer. 11. (b) At the point (-1, 2), the value of d²y is -12. Find the second-degree Taylor polynomial for fabout x = -1. (c) Find the particular solution y = f(x) to the given differential equation with the initial condition f(-1) = 2.
Transcribed Image Text:Free Response -BC (No Calculator) Consider the differential equation = 6x²-x²y. Let y = f(x) be a particular solution to this dx differential equation with the initial condition f(-1) = 2. (a) Use Euler's method with two steps of equal size, starting at x = -1, to approximate f(0). Show the work that leads to your answer. 11. (b) At the point (-1, 2), the value of d²y is -12. Find the second-degree Taylor polynomial for fabout x = -1. (c) Find the particular solution y = f(x) to the given differential equation with the initial condition f(-1) = 2.
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