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**Unformatted text preview: **executable program. Alternatively, the reader can use the software provided free with the text.) The inputs to the program are x = 0, y = 0, c = 1, = 0 . 003, and, say, M = 100. Notice that by Step 6 of the improved Eulers method with tolerance, the computations should terminate when two successive approximations dier by less that 0 . 003. The initial value for h in Step 1 of the improved Eulers method subroutine is h = (1 0)2 = 1 . For the given equation, we have f ( x, y ) = 1 y + y 3 , and so the numbers F and G in Step 3 145...

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