1550078481-Ordinary_Differential_Equations__Roberts_

The Laplace Transform Method 263 cannot solve easily using the method of undetermined coefficients (See sec- tion 4.4.). If we w ...

264 Ordinary Differential Equations SOLUTION Taking the Laplace transform of the differential equation in (2) and using the line ...

The Laplace Transf arm Method 265 ! sinx, y(x)= 2-2cos(x-l)+sinx, 1 - 2cos(x -1) + cos(x - 2) + sin x, -oo < x::::: 1 The rea ...

266 Ordinary Differential Equations Use Theorem 5.3 and Table 5.1 to find an inverse Laplace transform of the following functio ...

The Laplace Trans! orm Method h :=piecewise(x < 1, 0, 1 < = x and x < 2, 2, 2 < = x, 1): h := convert(%, Heaviside); ...

268 Ordinary Differential Equations where Eis a small positive constant. A graph of one function d, (x) is shown in Figure 5. 7. ...

The Laplace Trans! arm Method 269 and 1-: 5 ( x - c) dx = l. Let f(x) be a function which is continuous on some interval about x ...

270 Ordinary Differential Equations by an impulse force. Taking the Laplace transform of the given differential equation and imp ...

The Laplace Transform Method EXAMPLE 2 Solving an Initial Value Problem with an Impulse Forcing Function Solve the initial value ...

272 Ordinary Differential Equations y(x) = ~u(x - 2)e-(x-^2 ) sin 2(x - 2) + 4e-x cos 2x + 2e-x sin 2x 2 { 4e-x cos 2x + 2e-x si ...

The Laplace Trans! orm Method 273 EXERCISES 5.5 Find the solution of the following initial value problems using the Laplace tran ...

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Chapter 6 Applications of Linear Differential Equations with Constant Coefficients In this chapter we will examine a few linear ...

276 Ordinary Differential Equations value problem (1) my"+cy'+ksiny=O; y(O)=co, y' (O)=c1 where c ~ O is a constant of proportio ...

Applications of Linear Equations with Constant Coefficients 277 that produces the elongation or compression. (The Englishman Rob ...

278 Ordinary Differential Equations The spring-mass mechanical systems ( 4) and ( 5) may be set in motion (i) by pulling the mas ...

Applications of Linear Equations with Constant Coefficients 279 The electric charge, q, and the current, i = dq/ dt, are functio ...

280 Ordinary Differential Equations Substituting i = dq/dt = q' into equation (6), we find that the charge on the capacitor, q, ...

Applications of Linear Equations with Constant Coefficients 281 Table 6.2 Correspondence between electrical and mechanical syste ...

282 Ordinary Differential Equations 6.1.1.1 Free Undamped Motion Furthermore, when there is no damping force acting on the syste ...