Private Sector Involvement and International Financial Crises: An Analytical Perspective

By Michael Chui; Prasanna Gai | Go to book overview

Appendix A Solution to the First-Order Differential Equation

This appendix illustrates the mathematical methods needed to solve equation (4.6), a first-order differential equation. Readers are referred to textbooks such as Chiang (1984) for more rigorous treatments.

We first re-arrange (4.6) into:(A.1)

To derive the general solution of (A.1), we first multiply it by an integrating factor, I, to make it an exact equation.(A.2)

Consider the following first-order differential equation,(A.3)

which is said to be exact if and only if:(A.4)

Thus, for (A.2) to be exact,(A.5)

On solving, the integrating factor equals:

-187-

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Private Sector Involvement and International Financial Crises: An Analytical Perspective
Table of contents

Table of contents

  • Private Sector Involvement and International Financial Crises: An Analytical Perspective iii
  • Foreword v
  • Preface vii
  • Contents ix
  • List of Figures xi
  • List of Tables xiii
  • Part I the Analytics of Crisis 13
  • Part II Reforming the International Financial Architecture 103
  • Appendix a Solution to the First-Order Differential Equation 187
  • Bibliography 195
  • Index 205
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