dy, = y2 dt 9 Consider the linear system dy2 -Yı dt Find the solution of this system which satisfies the conditions y, (0) = 0, y, (0) = 1 Find the solution of this system which satisfies the conditions y, (0) = -1, y,(0) = 0 Show that the two different solutions found in a),b) both represent the same path.

dy, = y2 dt 9 Consider the linear system dy2 -Yı dt Find the solution of this system which satisfies the conditions y, (0) = 0, y, (0) = 1 Find the solution of this system which satisfies the conditions y, (0) = -1, y,(0) = 0 Show that the two different solutions found in a),b) both represent the same path.

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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Question

dy
= y2
dt
.9 Consider the linear system
dy,
= -
dt
Find the solution of this system which satisfies the conditions
y, (0) = 0, y, (0) =1
Find the solution of this system which satisfies the conditions
y, (0) = -1, y, (0) = 0
Show that the two different solutions found in a),b) both represent
the same path.
Find the D.E which gives the slope of the tangent to the paths, and
solve it to obtain the one parameter family of paths.
Sketch a few of paths.

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