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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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