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Chapter 9: Linear Differential Equations

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Linear Algebra With Applications
Pages: 415 - 442
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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131 Questions for Chapter 9: Linear Differential Equations

  1. Question:Justify the “Rule of 69”: If a quantity grows at a constant instantaneous rate of, then its doubling time is about. Example: In 2008 the population of Madagascar was about 20 million, growing at an annual rate of about 3%, with a doubling time of about 69/3 = 23 years.

    Found on Page 426

  2. Sketch rough phase portraits for the dynamical systems given in Exercise 32 through 39.

    Found on Page 427

  3. Consider a quadratic formq(x→)=x→·Ax→of two variables. Consider the system of differential equationsdx1dt=∂q∂x1dx2dt=∂q∂x2

    Found on Page 437

  4. Solve the nonlinear differential equations in Exercises 6through 11 using the method of separation of variables:Write the differential equation dxdt=fxas dxfx=dtand integrate both sides.

    Found on Page 425

  5. Do parts a and d of Exercise 10 for a quadratic form of n variables

    Found on Page 437

  6. Solve the nonlinear differential equations in Exercises 6through 11 using the method of separation of variables:Write the differential equation dxdt=fxas dxfx=dtand integrate both sides.

    Found on Page 425

  7. Find a differential equation of the formdxdt=kxfor which x(t)=3tis a solution.

    Found on Page 425

  8. Solve the differential equationf"(t)-4f'(t)+13f(t)=0and find all the real solutions of the differential equation.

    Found on Page 442

  9. Determine the stability of the systemdx→dt=(000001-1-1-2)x→

    Found on Page 439

  10. If the systemdx→dt=Ax→is stable, isdx→dt=A-1x→stable as well? How can you tell?

    Found on Page 439

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