State whether or not the following two differential equations are autonomous. Identify all the equilibrium solutions (if any). Sketch the direction field for the differential equation in the rectangular grid -5 < x < 5, –5 < y < 5 on the ry-plane with Ax = 1 and Ay = 1 ONLY for the autonomous one(s). Sketch a rough solution curve that passes through (-2, –1) ONLY for the au- tonomous one(s). (i) y = y² – x (ii) y' = y² – 4

State whether or not the following two differential equations are autonomous. Identify all the equilibrium solutions (if any). Sketch the direction field for the differential equation in the rectangular grid -5 < x < 5, –5 < y < 5 on the ry-plane with Ax = 1 and Ay = 1 ONLY for the autonomous one(s). Sketch a rough solution curve that passes through (-2, –1) ONLY for the au- tonomous one(s). (i) y = y² – x (ii) y' = y² – 4

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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State whether or not the following two differential equations are autonomous.
Identify all the equilibrium solutions (if any).
Sketch the direction field for the differential equation in the rectangular grid
-5 < x < 5, –5 < y < 5 on the ry-plane with Ax = 1 and Ay = 1 ONLY for
the autonomous one(s).
Sketch a rough solution curve that passes through (-2, –1) ONLY for the au-
tonomous one(s).
(i) y = y² – x
(ii) y' = y² – 4

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