1550078481-Ordinary_Differential_Equations__Roberts_

N-th Order Linear Differential Equations 183 Since y(x) satisfies the DE (26) and contains no arbitrary constant, y(x) is a part ...

184 Ordinary Differential Equations of the nonhomogeneous DE (24). Observe that the complementary solution is the general soluti ...

N-th Order Linear Differential Equations 185 The following theorem summarizes the results we obtained in this section. SUMMARY T ...

186 Ordinary Differential Equations EXERCISES 4.1 In exercises 1-6 determine the largest interval on which the exis- tence and u ...

N-th Order Linear Differential Equations 187 13. a. Verify that Y1 = ex and Y2 = ex are linearly independent solutions on (-oo, ...

188 Ordinary Differential Equations 17. a. Verify that YP = 3x + 2 is a particula r solution on (-oo, oo) of the nonhomogeneous ...

N-th Order Linear Differential Equations 189 DEFINITIONS Polynomial and Root of a Polynomial A polynomial of degree n in one var ...

190 Ordinary Differential Equations that the various sets of numbers- natural, rational, real, and complex- were themselves in t ...

N-th Order Linear Differential Equations 191 imaginary. In 1748 , Euler introduced the use of i for A and in 1832, Gauss gave th ...

192 Ordinary Differential Equations his students, Ludovico Ferrari, who claimed Cardan received the solution from Ferro through ...

N-th Order Linear Differential Equations 193 If (3) x1 > fa, then fax1 >a and fa> a/x 1. Case (2) states if x 1 is less ...

194 Ordinary Differential Equations line. See Figure 4.1. The equation of the tangent line at (x1, f(x1))- that is, the equation ...

N-th Order Linear Differential Equations 195 Consider the polynomial equation f(x) = x^2 - a= 0 where a > 0. Differ- entiatin ...

196 Ordinary Differential Equations Solving the set of equations (1) for the a's, we get an= bn-l an-l = bn-2 - bn-lt a2 = b1 - ...

N-th Order Linear Differential Equations 197 Use equations (1) and (2) to compute R = p(tn) and S = p'(tn) for n=l,2,3, .... Pr ...

198 Ordinary Differential Equations learn is how to interpret results from a computer. When a p olynomial has repeated real root ...

N-th Order Linear Differential Equations 199 EXERCISES 4.2 In the following exercises use POLYRTS or computer routines available ...

200 Ordinary Differential Equations About 1600, the French lawyer, politician, and part-time mathemati- cian, Frarn;ois Viete i ...

N-th Order Linear Differential Equations L I I T e I -+ iA Vertical 1 ' ' / ' / / Fg=mg Figure 4.4 A Simple P endulum 201 The ne ...

202 Ordinary Differential Equations The Maclaurin expansion for sine is e3 e5 sine = e - - + - - .... 3! 5! Fore small, sine is ...