165_pdfsam_math 54 differential equation solutions odd

165_pdfsam_math 54 differential equation solutions odd - ....

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Exercises 3.7 –3 –2 –1 0 0.5 1 1.5 2 2.5 3 y x Figure 3–C : Polygonal line approximation to the solution of y 0 =cos(5 y ) x , y (0) = 0, on [0 , 3]. 15. Here f ( x, y )=cos(5 y ) x , x 0 =0 ,and y 0 = 0. With a step size h =0 . 1wetake N =30in order to approximate the solution on [0 , 3]. We set x = x 0 =0 , y = y 0 = 0 and compute k 1 = hf ( x, y )=0 . 1[cos(5 · 0) 0] = 0 . 1; k 2 = hf ( x + h/ 2 ,y + k 1 / 2) = 0 . 1[cos(5(0 + 0 . 1 / 2)) (0 + 0 . 1 / 2)] = 0 . 091891 ; k 3 = hf ( x + h/ 2 ,y + k 2 / 2) = 0 . 1[cos(5(0 + 0 . 091891 / 2)) (0 + 0 . 1 / 2)] = 0 . 092373 ; k 4 = hf ( x + h, y + k 3 )=0
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Unformatted text preview: . 092373)) (0 + 0 . 1)] = 0 . 079522 ; x = 0 + 0 . 1 = 0 . 1 , y = 0 + 1 6 (0 . 1 + 2 . 091891 + 2 . 092373 + 0 . 079522) . 091342 ; . . . The results of computations are shown in Table 3-J. Using these value, we sketch a polygonal line approximating the graph of the solution on [0 , 3]. See Figure 3-C. 161...
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