1550078481-Ordinary_Differential_Equations__Roberts_

The Laplace Transform Method 243 du= -se-sxdx and v = y'(x). Substituting these expressions into the formula for integration by ...

244 Ordinary Differential Equations SOLUTION Apply the Laplace Transform to the Differential Equation Taking the Laplace transfo ...

The Laplace Trans/ arm Method EXAMPLE 2 Using the Laplace Transform to Solve a Nonhomogeneous Linear Differential Equation 245 F ...

246 Ordinary Differential Equations Apply the Inverse Laplace Transform Applying the inverse Laplace transform to (7) and using ...

The Laplace Trans/ orm Method 247 Using partial fraction expansion, results in (lO) £[ (x)] __ l __ ~_l __ ~_s __^17 1 1 (s - 2) ...

248 Ordinary Differential Equations the proper syntax requesting a CAS to use the Laplace transform method to solve the initial ...

The Laplace Trans! arm Method 249 !comments on Computer Software! The following nine MAPLE state- ments calculate and print the ...

250 Ordinary Differential Equations The following three MAPLE statements calculate and print the general solution of the differe ...

The Laplace Trans] orm Method 251 DEFINITION Convolution of f(x) and g(x) The convolution of f(x) and g(x) is (1) j(x) * g(x) =f ...

252 Ordinary Differential Equations of integration is shown in Figure 5.2a. Assuming that the order of integration can b e inter ...

The Laplace Trans] orm Method EXAMPLE 1 Using the Convolution Theorem to Find an Inverse Laplace Transform 1 Find a function h(x ...

254 Ordinary Differential Equations SOLUTION By the partial fraction expansion, there exist constants A, B , and C such that 1 A ...

The Laplace Tmnsf orm Method 255 Solving for .C[y(x)], we find the Laplace transform of the solution, y(x), of the given initial ...

256 Ordinary Differential Equations 11. y" -y' - 2y = O; y(O) = 0, y'(O) = 3 (HINT: See exercise 2.) 11 1 y" - y' - 2y = x^2 ; ...

The Laplace Trans! orm Method 5.4 The Unit Function and Time-Delay Function 257 The Laplace transform method is useful not only ...

258 Ordinary Differential Equations a. y(x) u(x - 1) -4 -2 T x 2 4 b. y(x) 2u(x-1) -4 -2 T x 2 4 c. y(x) -u(x - 2) T x -2 -4 2._ ...

The Laplace Trans! arm Method 259 Jump discontinuities occur in physical problems such as electrical circuits which include "on/ ...

260 Ordinary Differential Equations a. y(x) = cos x -1.5 1.5 y 1 0.5 b. y(x) = [u(x -n) -u(x -2n)] - 2^0 2 4 6 -0.5 -1 -1.5 1.5 ...

The Laplace Trans/ arm Met hod 261 x c a. b. x Figure 5.6 The Function f(x) and Associated c-time Delay Function g(x) The follow ...

262 Ordinary Differential Equations SOLUTION Using the trigonometric identity cos(x - 7r) = - cosx, we see that f(x) = cosx - u( ...