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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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part D only

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.
Expert Solution
Step 1

Given: The direction field for dydx=25x9y

Find the behavior of the solution as x→+∞ and x→-∞

Variable separable method:

dydx=f1xg2y then ∫g2ydy=∫f1xdx

 

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