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Yn+1(x) = A + f" de dt F(t, yn (t)), yo(x) = A, a is erate of the solution to (a) Use the iterative formula (3.12) to show that the second it- n = 0, 1, dy dx y(x) = A + x + (3.12) = 1 + xy², y(0) = A, x ≥ 0, 2 + ½ A²z² + ²Ax³ + = (1 + A³) zª + A²z³ + — A¹2º.

Yn+1(x) = A + f" de dt F(t, yn (t)), yo(x) = A, a is erate of the solution to (a) Use the iterative formula (3.12) to show that the second it- n = 0, 1, dy dx y(x) = A + x + (3.12) = 1 + xy², y(0) = A, x ≥ 0, 2 + ½ A²z² + ²Ax³ + = (1 + A³) zª + A²z³ + — A¹2º.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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Yn+1(x) = A + f" a dt F(t, yn (t)), yo(x) = A, is erate of the solution to n = 0, 1, (a) Use the iterative formula (3.12) to show that the second it- dy dx (3.12) = 1 + xy², y(0) = A, x ≥ 0, 2 y(x) = A + x + + }{A³²x³² + ¾=Aa² + ½ (¹ + A²³) x² + }=A²³x³ + — Aªzº. · (1 A¹x6 24
Transcribed Image Text:Yn+1(x) = A + f" a dt F(t, yn (t)), yo(x) = A, is erate of the solution to n = 0, 1, (a) Use the iterative formula (3.12) to show that the second it- dy dx (3.12) = 1 + xy², y(0) = A, x ≥ 0, 2 y(x) = A + x + + }{A³²x³² + ¾=Aa² + ½ (¹ + A²³) x² + }=A²³x³ + — Aªzº. · (1 A¹x6 24
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