Page 227 - Schaum's Outline of Differential Equations

210 SOLVING SECOND-ORDER DIFFERENTIAL EQUATIONS [CHAP. 20

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20.17. Reduce the initial-value problem 2yy"- 4xy y' + 2(sin x)y 4 = 6; (l) = 0, /(I) = 15 to system (20.1).
y
2
20.18. Reduce the initial-value problem xy'" - x y" + (y'fy = 0; y(0) = 1, /(O) = 2, y"(0) = 3 to system (20.2).
20.19. Use Euler's method with h = 0.1 to solve the initial-value problem given in Problem 20.15 on the interval [0, 1].
20.20. Use Euler's method with h = 0.1 to solve the initial-value problem given in Problem 20.16 on the interval [0, 1].
20.21. Use the Runge-Kutta method with h = 0.1 to solve the initial-value problem given in Problem 20.15 on the interval
[0, 1].
20.22. Use the Runge-Kutta method with h = 0.1 to solve the initial-value problem given in Problem 20.16 on the interval
[0, 1].
20.23. Use the Adams-Bashforth-Moulton method with h = 0.1 to solve the initial-value problem given in Problem 20.2
on the interval [0, 1]. Obtain appropriate starting values from Table 20-4.
20.24. Use the Adams-Bashforth-Moulton method with h = 0.1 to solve the initial-value problem given in Problem 20.15
on the interval [0, 1].
20.25. Use the Adams-Bashforth-Moulton method with h = 0.1 to solve the initial-value problem given in Problem 20.16
on the interval [0, 1].
20.26. Use Milne's method with h = 0.1 to solve the initial-value problem given in Problem 20.2 on the interval [0, 1].
Obtain appropriate starting values from Table 20-4.
20.27. Use Milne's method with h = 0.1 to solve the initial-value problem given in Problem 20.15 on the interval [0, 1].
20.28. Formulate the modified Euler's method for System (20.1).
20.29. Formulate the Runge-Kutta method for System (20.2).
20.30. Formulate Milne's method for System (20.2).