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(d) What can be said about the behavior of the above solutions as x→ + co? How about x--co?

(d) What can be said about the behavior of the above solutions as x→ + co? How about x--co?

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 12CR
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The direction field for dy 25x dx gy = 5 (a) Verify that the straight lines y = 3x are solution curves, provided x#0. is shown to the right. (b) Sketch the solution curve with initial condition y(0) = -1. (c) Sketch the solution curve with initial condition y(3) = 1. (d) What can be said about the behavior of the above solutions as x→ + co? How about x→-co? dy 0. dx (Simplify your answer.) 25x (a) The restriction y#0 is needed because is not defined when y = 0. Consider the straight lines one at a time. First let y = 9y dy 25x Substituting the expression for y into the differential equation yields dx 9 5 The result from the previous step simplifies to verifying that the straight line y = 3x is (Simplify your answer.) Now let y=-- (Simplify your answer.) 5 x. In this case, the standard rules of differentiation yield 3x dy dx = 17. 25x dy Substituting the expression for y into the differential equation yields dx 9( is a solution curve.
Transcribed Image Text:The direction field for dy 25x dx gy = 5 (a) Verify that the straight lines y = 3x are solution curves, provided x#0. is shown to the right. (b) Sketch the solution curve with initial condition y(0) = -1. (c) Sketch the solution curve with initial condition y(3) = 1. (d) What can be said about the behavior of the above solutions as x→ + co? How about x→-co? dy 0. dx (Simplify your answer.) 25x (a) The restriction y#0 is needed because is not defined when y = 0. Consider the straight lines one at a time. First let y = 9y dy 25x Substituting the expression for y into the differential equation yields dx 9 5 The result from the previous step simplifies to verifying that the straight line y = 3x is (Simplify your answer.) Now let y=-- (Simplify your answer.) 5 x. In this case, the standard rules of differentiation yield 3x dy dx = 17. 25x dy Substituting the expression for y into the differential equation yields dx 9( is a solution curve.
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