Solution Found!
The direction field for is shown in dy/dx = 4x/y Figure
Chapter 1, Problem 2E(choose chapter or problem)
Problem 2E
Problem
The direction field for is shown in dy/dx = 4x/y Figure 1.13.
(a) Verify that the straight lines y = ± 2x are solution curves, provided x ≠ 0.
(b) Sketch the solution curve with initial condition y (0) = 2.
(c) Sketch the solution curve with initial condition y(2) = 1.
(d) What can you say about the behavior of the above solutions as x + ∞? How about - ∞
Questions & Answers
QUESTION:
Problem 2E
Problem
The direction field for is shown in dy/dx = 4x/y Figure 1.13.
(a) Verify that the straight lines y = ± 2x are solution curves, provided x ≠ 0.
(b) Sketch the solution curve with initial condition y (0) = 2.
(c) Sketch the solution curve with initial condition y(2) = 1.
(d) What can you say about the behavior of the above solutions as x + ∞? How about - ∞
ANSWER:
Solution :
Step 1 ;
In this problem given that
- Consider
Given that the straight lines
is verified.
Then the below graph shows the solution equation .
