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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 = yo+y ५. XX0 + 2D 0.5+ 20 y' = 1-²-y(2) = -1, dx = 0.5.

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 = yo+y ५. XX0 + 2D 0.5+ 20 y' = 1-²-y(2) = -1, dx = 0.5.

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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(Leave Q1 to Q10, Q21 to Q42} 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 = Yo + y X₂= xo + 2DX 0.5+ 2015) (only questions Q11-Q20 Required) y'=1--y(2) = -1, dx = 0.5. X Sol. y₁=yo+(1-2) dx = -1 + (1-¹) 4.5) = -0.25, Y2 = y₁ + (1-4) dx = -0.25+ (1--235) 0.5) - 0.3, Y3 = y₂ + (1-2) dx = 0.3 + (1 - 93) 6.5) = 0.75; +() y = 1 + P(x) = Q(x) == P(x) dx = S dx = ln |x| = ln x, x > 0 ⇒ v(x) = enx = ⇒ y = √x - 1 dx = ( + C) ; x = 2, y = -1 ⇒ −1 = 1 + ⇒ C=y=-1 ⇒y(3.5)= 35 - 35 = 4.25 0.6071 Q14: Use Euler's method to calculate the first three approximations to the given initia 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. y' = y² (1 + 2x), y(-1) = 1, dx = 0.5
Transcribed Image Text:(Leave Q1 to Q10, Q21 to Q42} 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 = Yo + y X₂= xo + 2DX 0.5+ 2015) (only questions Q11-Q20 Required) y'=1--y(2) = -1, dx = 0.5. X Sol. y₁=yo+(1-2) dx = -1 + (1-¹) 4.5) = -0.25, Y2 = y₁ + (1-4) dx = -0.25+ (1--235) 0.5) - 0.3, Y3 = y₂ + (1-2) dx = 0.3 + (1 - 93) 6.5) = 0.75; +() y = 1 + P(x) = Q(x) == P(x) dx = S dx = ln |x| = ln x, x > 0 ⇒ v(x) = enx = ⇒ y = √x - 1 dx = ( + C) ; x = 2, y = -1 ⇒ −1 = 1 + ⇒ C=y=-1 ⇒y(3.5)= 35 - 35 = 4.25 0.6071 Q14: Use Euler's method to calculate the first three approximations to the given initia 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. y' = y² (1 + 2x), y(-1) = 1, dx = 0.5
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