hw3solns - = 1 1 + sin(0 . 2) = . 834258 y (0 . 3) = 1 1 +...

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Section 2.5 3. dy dx = - y 2 cos x , h = 0 . 1, y (0) = 1; explicit solution y = 1 1 + sin x . x 0 = 0 x 1 = 0 + (0 . 1)(1) = 0 . 1 x 2 = 0 + (0 . 1)(2) = 0 . 2 x 3 = 0 + (0 . 1)(3) = 0 . 3 x 4 = 0 + (0 . 1)(4) = 0 . 4 y 0 = 1 y 1 = 1 + (0 . 1)( - (1) 2 cos(0)) = . 9 y 2 = . 9 + (0 . 1)( - ( . 9) 2 cos(0 . 1)) = . 8194 y 3 = . 8194 + (0 . 1)( - ( . 8194) 2 cos(0 . 2)) = . 7536 y 4 = . 7536 + (0 . 1)( - ( . 7536) 2 cos(0 . 3)) = . 6993 Explicit: y (0) = 1 1 + sin 0 = 1 y (0 . 1) = 1 1 + sin(0 . 1) = . 909228 y (0 . 2)
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Unformatted text preview: = 1 1 + sin(0 . 2) = . 834258 y (0 . 3) = 1 1 + sin(0 . 3) = . 7718907 y (0 . 4) = 1 1 + sin(0 . 4) = . 719725 Euler Explicit x i y i y ( x i ) 0.0 1 1 0.1 .9 .909228 0.2 .8194 .834258 0.3 .7536 .7718907 0.4 .6993 .719725...
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