Consider the differential equation = 2xy². Let f(x) be the particular solution with ƒ (1) = 2. a) Write the equation for the tangent line to f(x) at x = 1. Use the tangent line to approximate ƒ(2). b) Use Euler's Method with 2 steps of equal size to approximate ƒ(2). Show your work. d²y c) At the point (1, 2) it is known that d= 72. Write the second-degree Taylor polynomial for dx² f(x) centered at x = 1. Use the Taylor polynomial to approximate ƒ(2).
Consider the differential equation = 2xy². Let f(x) be the particular solution with ƒ (1) = 2. a) Write the equation for the tangent line to f(x) at x = 1. Use the tangent line to approximate ƒ(2). b) Use Euler's Method with 2 steps of equal size to approximate ƒ(2). Show your work. d²y c) At the point (1, 2) it is known that d= 72. Write the second-degree Taylor polynomial for dx² f(x) centered at x = 1. Use the Taylor polynomial to approximate ƒ(2).
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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Transcribed Image Text:3. Consider the differential equation
dx
dy
= 2xy². Let f(x) be the particular solution with f(1) = 2.
a) Write the equation for the tangent line to f (x) at x = 1. Use the tangent line to approximate
f(2).
b) Use Euler's Method with 2 steps of equal size to approximate f (2). Show your work.
c) At the point (1, 2) it is known that
= 72. Write the second-degree Taylor polynomial for
dx²
f(x) centered at x = 1. Use the Taylor polynomial to approximate f(2).
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