1550078481-Ordinary_Differential_Equations__Roberts_

542 Ordinary Differential Equations

7. y = 1 + ~ ln 3 + ~ ln I x -

1

1 · ( 1, oo)

2 2 x+l '

9. y = -ln I cos x i ; (-7r / 2, 7r / 2)

Exercises 2.3.2 Solution of the Separable Equation y' = g(x)/h(y)

1. y = -e3x ; ( - oo, CXl) 3. y = 1 + e-x; ( - oo, CXl)


2. y = -2x; ( -oo, 0) 7. y = 2/( 1 + e^2 x) ; ( - oo, CXl)

9.

x2

y = - ln(

2

+ 1) ; ( - oo, CXl)

Exercises 2.3.3 Solution of the Linear Equation y' = a(x)y + b(x)

1. y = (5e^4 x - 1)/4; (-oo, oo) 3. y = -2x ; (-oo, 0)

x sin t^2

5. y = x(l + J_ 1 -t-dt) ; (-oo, 0) 7. y = (x-7r/2)sinx; (0 ,7r)


6. 40°F 11. A 13. y = Cx


7. y=Cx/(x+l)^3

Exercises 2.4 Numerical Solution

Exercises 2.4.1 Single-Step Methods

1. a.

Yn+l = h~/3+(l-hn+h;/2-h~/6)yn+(h;-h~/3)xn+(hn-h;/2+h~/6)x;