Exercise 2.3.2 Use whatever technology you have available to sketch a direction field for the given ODE on the specified range. If the ODE is autonomous, visually identify the equilibrium solutions, if any. (a) u' (t) = u(t)-2t for 0 ≤t≤2 and 0 ≤ u ≤ 2. (b) u'(t)=u²(1)+1+1 for -2 <1 ≤ 2 and -2 ≤u≤ 2. (c) u' (t)=-u(t) for -2 ≤t≤2 and -2 ≤ u ≤ 2. (d) u'(t) = -1/u(t) for -2 ≤t≤2 and -2 ≤ u≤ 2. (e) u'(t) = u(t) (u(t)-3) for -2≤t ≤5 and -2 ≤u≤ 5. (f) u' (t) = (u(t)-1) (u(t) +1) for -2 <1 ≤5 and -2 ≤u≤5. (g) u' (t)=tsin(u)-12/4,-2 ≤t≤5 and -2 ≤u≤5. (h) u' (t) = cos(u+1) for -2 <1 ≤5 and -2 ≤ u ≤ 5. Exercise 2.3.3 For each ODE sketch a phase portrait by hand, following the procedure of Examples 2.10.2.11, and 2.12. Classify each fixed point as asymptotically stable or unstable. b,d and g

Exercise 2.3.2 Use whatever technology you have available to sketch a direction field for the given ODE on the specified range. If the ODE is autonomous, visually identify the equilibrium solutions, if any. (a) u' (t) = u(t)-2t for 0 ≤t≤2 and 0 ≤ u ≤ 2. (b) u'(t)=u²(1)+1+1 for -2 <1 ≤ 2 and -2 ≤u≤ 2. (c) u' (t)=-u(t) for -2 ≤t≤2 and -2 ≤ u ≤ 2. (d) u'(t) = -1/u(t) for -2 ≤t≤2 and -2 ≤ u≤ 2. (e) u'(t) = u(t) (u(t)-3) for -2≤t ≤5 and -2 ≤u≤ 5. (f) u' (t) = (u(t)-1) (u(t) +1) for -2 <1 ≤5 and -2 ≤u≤5. (g) u' (t)=tsin(u)-12/4,-2 ≤t≤5 and -2 ≤u≤5. (h) u' (t) = cos(u+1) for -2 <1 ≤5 and -2 ≤ u ≤ 5. Exercise 2.3.3 For each ODE sketch a phase portrait by hand, following the procedure of Examples 2.10.2.11, and 2.12. Classify each fixed point as asymptotically stable or unstable. b,d and g

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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