144_pdfsam_math 54 differential equation solutions odd

# 144_pdfsam_math 54 differential equation solutions odd -...

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Chapter 3 Euler’s method is defned by equation (4) on page 125 oF the text to be y n +1 = y n + hf ( x n ,y n ) ,n =0 , 1 , 2 ,... , where f ( x, y )=5 y . Starting with the given value oF y 0 = 1, we compute y 1 = y 0 + h (5 y 0 )=1+5 h. We can then use this value to compute y 2 to be y 2 = y 1 + h (5 y 1 )=(1+5 h ) y 1 =(1+5 h ) 2 . Proceeding in this manner, we can generalize to y n : y n h ) n . ReFerring back to our equation For x n and using the given values oF x 0 =0and x 1 = 1 we fnd 1= nh n = 1 h . Substituting this back into the Formula For y n we fnd the approximation to the initial value problem y 0 =5 y, y (0) = 1 at x = 1 to be (1 + 5 h ) 1 /h . 3. In this initial value problem, f ( x, y )= y , x 0 ,and y 0 = 1. ±ormula (8) on page 127 oF the text then becomes y n +1
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## This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.

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