MY NOTESPRACTICE ANOTHERUse Euler's method to obtain a four-decimal approximation of the indicatedvalue. Carry out the recursion of (3) in Section 2.6Yn +1 = Yn + hf(Xni Yn)by hand, first using h = 0.1 and then using h = 0.05.(3)y' = 2x – 3y + 1, y(1) = 6; y(1.2)y(1.2) = 3.47(h = 0.1)y(1.2) = 3.6326437 X(h = 0.05)Need Help?Read ItWatch It

Given: dydx=2x-3y+1, y(1)=6 f(x,y)=2x-3y+1, x0=1, y0=6, h=0.1…

Answered: Jse Euler's method to obtain a…

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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MY NOTES
PRACTICE ANOTHER
Use Euler's method to obtain a four-decimal approximation of the indicated
value. Carry out the recursion of (3) in Section 2.6
Yn +1 = Yn + hf(Xni Yn)
by hand, first using h = 0.1 and then using h = 0.05.
(3)
y' = 2x – 3y + 1, y(1) = 6; y(1.2)
y(1.2) = 3.47
(h = 0.1)
y(1.2) = 3.6326437 X
(h = 0.05)
Need Help?
Read It
Watch It

Expert Solution

Step 1

Given:

$\frac{d y}{d x} = 2 x - 3 y + 1, y (1) = 6$

$f (x, y) = 2 x - 3 y + 1, x_{0} = 1, y_{0} = 6, h = 0.1$

$y_{1} = y (1.1) = y_{0} + h f (x_{0}, y_{0}) y_{1} = y (1.1) = 6 + 0.1 \times (2 \times 1 - 3 \times 6 + 1) y_{1} = y (1.1) = 6 + 0.1 \times - 15 y_{1} = y (1.1) = 4.5 y_{2} = y (1.2) = y_{1} + h f (x_{1}, y_{1}) y_{2} = y (1.2) = 4.5 + 0.1 (2 \times (1.1) - 3 \times (4.5) + 1) y_{2} = y (1.2) = 4.5 + 0.1 \times (2.2 - 13.5 + 1) y_{2} = y (1.2) = 4.5 - 1.03 y_{2} = 3.47$

$\Rightarrow y (1.2) = 3.47$

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