Consider the differential equation y' = 2y X a) Sketch the slope-field for x in [−2, 2] and y in [0, 4]. Sketch several (at least 10) slope vectors in both quadrants. In particular, find the slope at each point below, and plot those slope vectors. (−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4) . To be clear, I want you to write down the slope at each of the above points and plot slope vectors at those points in a table. In addition, I want you to plot several additional slope vectors at some random points. b) Using your slope field and your table above, sketch the solution curve to y(x) with the initial value y(0) = 0. c) This differential equation is separable. It is also linear, first order. Solve the differential equation and solve the IVP problem y(0) = 0. Compare your solution to this part with your sketch in part b.
Consider the differential equation y' = 2y X a) Sketch the slope-field for x in [−2, 2] and y in [0, 4]. Sketch several (at least 10) slope vectors in both quadrants. In particular, find the slope at each point below, and plot those slope vectors. (−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4) . To be clear, I want you to write down the slope at each of the above points and plot slope vectors at those points in a table. In addition, I want you to plot several additional slope vectors at some random points. b) Using your slope field and your table above, sketch the solution curve to y(x) with the initial value y(0) = 0. c) This differential equation is separable. It is also linear, first order. Solve the differential equation and solve the IVP problem y(0) = 0. Compare your solution to this part with your sketch in part b.
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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![Consider the differential equation y'
=
2y
x
a) Sketch the slope-field for x in [-2, 2] and y in [0, 4]. Sketch several (at least
10) slope vectors in both quadrants. In particular, find the slope at each point
below, and plot those slope vectors.
(−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4) .
To be clear, I want you to write down the slope at each of the above points and
plot slope vectors at those points in a table. In addition, I want you to plot
several additional slope vectors at some random points.
b) Using your slope field and your table above, sketch the solution curve to
y(x) with the initial value y(0) = 0.
c) This differential equation is separable. It is also linear, first order. Solve the
differential equation and solve the IVP problem y(0) = 0. Compare your
solution to this part with your sketch in part b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2255e29a-5a2a-4583-8da4-49ff5d60466d%2Fb109c9d5-600d-4bf5-a4a0-8129b1c52056%2F9ot8hte_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the differential equation y'
=
2y
x
a) Sketch the slope-field for x in [-2, 2] and y in [0, 4]. Sketch several (at least
10) slope vectors in both quadrants. In particular, find the slope at each point
below, and plot those slope vectors.
(−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4) .
To be clear, I want you to write down the slope at each of the above points and
plot slope vectors at those points in a table. In addition, I want you to plot
several additional slope vectors at some random points.
b) Using your slope field and your table above, sketch the solution curve to
y(x) with the initial value y(0) = 0.
c) This differential equation is separable. It is also linear, first order. Solve the
differential equation and solve the IVP problem y(0) = 0. Compare your
solution to this part with your sketch in part b.
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