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Chapter 4: Linear Second-Order Equations

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Fundamentals Of Differential Equations And Boundary Value Problems
Pages: 152 - 240
Fundamentals Of Differential Equations And Boundary Value Problems

Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

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Illustration

332 Questions for Chapter 4: Linear Second-Order Equations

  1. In Problems 9 and 10, find a particular solution first by undetermined coefficients, and then by variation of parameters. Which method was quicker?

    Found on Page 191

  2. Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation. y''-y'+y=et+t2

    Found on Page 186

  3. Find a particular solution to the differential equation.

    Found on Page 180

  4. Question: find a general solution to the given differential equation y''-y'-11y=0.

    Found on Page 164

  5. Undamped oscillators that are driven at resonance have unusual (and nonphysical) solutions.

    Found on Page 157

  6. Use the result of Problem 8 to prove that if the pendulum in Figure 4.18 on page 208 is released from rest at the angle 0<α<π, then |θ(t)|≤αfor all t.

    Found on Page 211

  7. In Problems 9 through 14, find a general solution to the given Cauchy–Euler equation for t>0.t2d2ydt2+2tdydt-6y=0

    Found on Page 199

  8. In the following problems, take g=32ft/sec2 for the U.S. Customary System and g=9.8m/sec2for the MKS system.

    Found on Page 228

  9. A 14– kg mass is attached to a spring with stiffness 8 N/m. The damping constant for the system is 14N-sec/m. If the mass is moved 1 m to the left of equilibrium and released,what is the maximum displacement to the right that it will attain?

    Found on Page 220

  10. Find a general solution to the given differential equation.u''+11u=0

    Found on Page 231

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