011: Use Euler's method to calculate the first three approximations to the given initial value problem for the specified increment size. Calculate the exact solution and investigate the accuracy of your approximations. Round your results to four decimal places. Y₁ = y₁+ y ५. Yo XX0 + 2D 0.5+ 20. y' = 1-²y(2) = -1, dx = 0.5. X Sol. y₁=yo+(1-2) dx = -1 + (1-¹)45)= Y2 = y₁ + (1 - 4) dx = -0.25 + (1--235) 0.5) y3 = y₂ + (1-2) dx = 0.3+(1-3) 6.5) = 0.75 Y3 y2 +(¹)y=1 P(x) = Q(x) =D=> [P(x) dx = S dx = ln |x| = ln x, x > 0 ⇒ v(x) = elnxx ⇒ y = √x + 1 dx = ( + C) ; x = 2, y = -1 4 / ⇒ −1 = 1 + ⇒ C=4y = - X )=0.3, ⇒y(3.5)= 3,5-3 = 4.250.6071 first three approximations to the given i
011: Use Euler's method to calculate the first three approximations to the given initial value problem for the specified increment size. Calculate the exact solution and investigate the accuracy of your approximations. Round your results to four decimal places. Y₁ = y₁+ y ५. Yo XX0 + 2D 0.5+ 20. y' = 1-²y(2) = -1, dx = 0.5. X Sol. y₁=yo+(1-2) dx = -1 + (1-¹)45)= Y2 = y₁ + (1 - 4) dx = -0.25 + (1--235) 0.5) y3 = y₂ + (1-2) dx = 0.3+(1-3) 6.5) = 0.75 Y3 y2 +(¹)y=1 P(x) = Q(x) =D=> [P(x) dx = S dx = ln |x| = ln x, x > 0 ⇒ v(x) = elnxx ⇒ y = √x + 1 dx = ( + C) ; x = 2, y = -1 4 / ⇒ −1 = 1 + ⇒ C=4y = - X )=0.3, ⇒y(3.5)= 3,5-3 = 4.250.6071 first three approximations to the given i
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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