By Lawrence Cunningham

**Using the methods of the easiest moneymakers to take a position wisely**

*"An clever and considerate guide."**BusinessWeek*

*". . . a welcome boost to the bookshelf of a person who desires to take keep watch over of his or her monetary life."*United Press International

The bestselling hardcover variation of *How to imagine Like Benjamin Graham and make investments Like Warren Buffett *was broadly hailed for its common method of making clever funding offerings. This paperback model makes those similar instruments and strategies on hand to a much broader viewers. Explaining how one can study funding ambitions according to sincere worth rather than hype and mirrors, Lawrence Cunningham's top-ranked publication reveals:

- How to invite worthy questions, and insist significant solutions
- Market-proven equipment for comparing managers and CEOs
- Value making an investment suggestions that made Warren Buffett a billionaireand ultra-modern no 1 investor

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**Example text**

But P(r fc+1 ) = Afc+1. 7. Let w(x) and Ì;(X) be functions that possess two continuous derivatives on an interval / and which are such that W(x; u, v) Φ 0 for x in /. Show that the equation ' y y' y" u(x) u\x) u"{x) = 0 v(x) v'(x) v"(x) is a linear homogeneous second-order differential equation for which u(x) and v(x) are solutions on /. 8. By using the result of Problem 7, construct a linear homogeneous secondorder differential equation that has the given functions as solutions on the given intervals.

F(x). 85) by e~r2X, differentiate M2 + 1 times, and then multiply through by eriX. , s. 86) where fs(x) is a polynomial of the same degree as ps(x), namely, Ms. 86) by e~rsX and differentiating Ms 38 I Linear Differential Equations times, we find that dxM' fs(x) = 0. But this is impossible, since fs(x) is of degree Ms. Hence our assumption that the n solutions were linearly dependent is false; they must be linearly independent. 88) the resulting set of n real solutions is still linearly independent.

Use the result of Problem 5 to find particular solutions of the equations in Problems 1(c) and 1(d). 7. If the function yp(x) is a solution of the equation P(D)y = Aeiax (A is real), then the real and imaginary parts of yp(x) are real solutions of the equations P(D)y = A cos ax, P(D)y = A sin ax, respectively. Use this fact to find particular solutions of the equations in Problems l(i) and l(j). 14 Applications In this section we shall consider some elementary problems in mechanics and in electric circuit theory that lead to initial value problems for linear differential equations.