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
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:Q11: 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
X=X0 + 2DX
places. Y₁ = you y
0.54 2015)
y' = 1-²
X
y(2)=-1, dx=
dx = 0.5.
Sol.
y₁ = y + (1-2) dx = -1 + (1-¹) 4.5)=-0.25,
Y2 = y₁ + (1-4) dx = -0.25+ (1--235) 0.5) 0.3,
Y3y2 + (1-2) dx = 0.3+(1-3) 6.5) -0.75;
+ (1) y = 1 + P(x) = Q(x) =D⇒ [P(x) dx
= Sdx = ln |x| = In x, x > 0 ⇒ v(x) = elnx-x
⇒ y = ¹ √x · 1 dx = ( + C) ; x = 2, y = − 1
1
dx
X
⇒ −1 = 1 +
-
⇒ y(3.5)=3,5
4
⇒ C=4y= 1 -
X
ext
- 3 = 4,250.6071
method to calculate the first three approximations to the given init
on and
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