.1  and then use  h = 0.05. y' = 3x − 4y + 3, y(1) =

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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Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use 

h = 0.1

 and then use 

h = 0.05.
y' = 3x − 4y + 3, y(1) = 3;  y(1.5)
h = 0.1     y(1.5)  
h = 0.05     y(1.5)
Expert Solution
Step 1

Here, in the question given the set of equations as: y' = 3x-4y+3. We have to calculate the four-decimal approximation of the indicated value. Now first we shall know about the improved Euler's method. In Euler's method, we approximate the function by a rectangular shape ( shown below):

Advanced Math homework question answer, step 1, image 1

To improve the approximation we use the improved approximation method. 

Steps in Improved Euler's method:

Step 1:

 K1 = f( tn, yn)

Step 2:

K2=f(tn+h, yn+hk1)

Step 3:

yn+1= yn+hk1+k22

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