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Often a radical change in the form of the solution of a differential equation corresponds to a very small change in either the initial condition or the equation itself. Find an explicit solution of the given initial-value problem. dy = (y - 1)2 + 0.04, y(0) = 1 dx y = Use a graphing utility to plot the graph of the solution in a neighborhood of (0, 1). Compare the graph with those obtained in Problems 39, 40, and 42 of Section 2.2. y y y 1.0015 1.0015 1.015 1.0010 1.0010 1.010 1.0005 1.0005 1.005 -0.015-0.010-0.005 0.005 0.0100.015 -0.015 -0.010-0.005 0.9995 0.005 0.010 0.015 -0.015-0.010-0.005 0.9995 0.005 0.010 0.015 0.995 0.9990 0.9990 0.990 0.9985 0.9985 0.985 y 1.015 1.010 1.005 -0.015 -0.010-0.005 0.995 0.005 0.010 0.015 0.990 0.985

Often a radical change in the form of the solution of a differential equation corresponds to a very small change in either the initial condition or the equation itself. Find an explicit solution of the given initial-value problem. dy = (y - 1)2 + 0.04, y(0) = 1 dx y = Use a graphing utility to plot the graph of the solution in a neighborhood of (0, 1). Compare the graph with those obtained in Problems 39, 40, and 42 of Section 2.2. y y y 1.0015 1.0015 1.015 1.0010 1.0010 1.010 1.0005 1.0005 1.005 -0.015-0.010-0.005 0.005 0.0100.015 -0.015 -0.010-0.005 0.9995 0.005 0.010 0.015 -0.015-0.010-0.005 0.9995 0.005 0.010 0.015 0.995 0.9990 0.9990 0.990 0.9985 0.9985 0.985 y 1.015 1.010 1.005 -0.015 -0.010-0.005 0.995 0.005 0.010 0.015 0.990 0.985

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.CR: Chapter 11 Review
Problem 33CR
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Often a radical change in the form of the solution of a differential equation corresponds to a very small change in either the initial condition or the equation itself. Find an explicit solution of the given initial-value problem. dy = (y – 1)2 + 0.04, y(0) = 1 dx y = Use a graphing utility to plot the graph of the solution in a neighborhood of (0, 1). Compare the graph with those obtained in Problems 39, 40, and 42 of Section 2.2. y y y 1.0015 1.0015 1.015 1.0010 1.0010 1.010 1.0005 1.0005 1.005 X X -0.015 -0.010-0.005 0.9995 -0.015-0.010–0.005 0.995 0.005 0.010 0.015 -0.015 -0.010-0.005 0.005 0.010 0.015 0.005 0.010 0.015 0.9995 0.9990 0.9990 0.990 0.9985 0.9985 0.985 y 1.015 1.010 1.005 -0.015 –0.010–0.005 0.005 0.010 0.015 0.9 0.990 0.985
Transcribed Image Text:Often a radical change in the form of the solution of a differential equation corresponds to a very small change in either the initial condition or the equation itself. Find an explicit solution of the given initial-value problem. dy = (y – 1)2 + 0.04, y(0) = 1 dx y = Use a graphing utility to plot the graph of the solution in a neighborhood of (0, 1). Compare the graph with those obtained in Problems 39, 40, and 42 of Section 2.2. y y y 1.0015 1.0015 1.015 1.0010 1.0010 1.010 1.0005 1.0005 1.005 X X -0.015 -0.010-0.005 0.9995 -0.015-0.010–0.005 0.995 0.005 0.010 0.015 -0.015 -0.010-0.005 0.005 0.010 0.015 0.005 0.010 0.015 0.9995 0.9990 0.9990 0.990 0.9985 0.9985 0.985 y 1.015 1.010 1.005 -0.015 –0.010–0.005 0.005 0.010 0.015 0.9 0.990 0.985
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