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295_pdfsam_math 54 differential equation solutions odd

295_pdfsam_math 54 differential equation solutions odd -...

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Exercises 5.3 k 2 , 1 = hf 2 ( t n , x 1; n , x 2; n ) = hx 1; n ( 1 + rx 2 1; n ) , k 1 , 2 = hf 1 t n + h 2 , x 1; n + k 1 , 1 2 , x 2; n + k 2 , 1 2 = h x 2; n + k 2 , 1 2 , k 2 , 2 = hf 2 t n + h 2 , x 1; n + k 1 , 1 2 , x 2; n + k 2 , 1 2 = h x 1; n + k 1 , 1 2 1 + r x 1; n + k 1 , 1 2 2 , k 1 , 3 = hf 1 t n + h 2 , x 1; n + k 1 , 2 2 , x 2; n + k 2 , 2 2 = h x 2; n + k 2 , 2 2 , k 2 , 3 = hf 2 t n + h 2 , x 1; n + k 1 , 2 2 , x 2; n + k 2 , 2 2 = h x 1; n + k 1 , 2 2 1 + r x 1; n + k 1 , 2 2 2 , k 1 , 4 = hf 1 ( t n + h, x 1; n + k 1 , 3 , x 2; n + k 2 , 3 ) = h ( x 2; n + k 2 , 3 ) , k 2 , 4 = hf 2 ( t n + h, x 1; n + k 1 , 3 , x 2; n + k 2 , 3 ) = h ( x 1; n + k 1 , 3 ) 1 + r ( x 1; n + k 1 , 3 ) 2 . Using these values, we find t n +1 = t n + h = t n + 0 . 1 , x 1; n +1 = x 1; n + 1 6 ( k 1 , 1 + 2 k 1 , 2 + 2 k 1 , 3 + k 1 , 4 ) , x 2; n +1 = x 2; n + 1 6 ( k 2 , 1 + 2 k 2 , 2 + 2 k 2 , 3 + k 2 , 4 ) . In Table 5-D we give the approximate period for r = 1 and 2 with a = 1, 2 and 3, from this we see that the period varies as r is varied or as a is varied. Table 5–D : Approximate period of the solution to Problem 23.
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