Reduction of order

Higher-Order Linear Equations and the Reduction of Order Method

Published in Kenneth B. Howell, Ordinary Differential Equations, 2019

14.3. Several nonhomogeneous differential equations are given below. For each, first verify that the given y1is a solution to the corresponding homogeneous differential equation, and then find the general solution to the given nonhomogeneous differential equation using reduction of order with the given y1. y″ − 4y′ + 3y = 9e2x, y1(x) = e3xy″ − 6y′ + 8y = e4x, y1(x) = e2xx2y″ + xy′− y=xon x > 0, y1(x) = xx2″− 20y = 27x5on x > 0, y1(x) = x5xy″ + (2 + 2x)y′ + 2y = 8e2xon x > 0, y1(x) = x−1(x + 1)y″ + xy′ − y = (x + 1)2, y1(x) = e−x

Pedogogical perspectives on the method of Wilmer III and Costa for solving second-order differential equations

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Journal Information

Published in International Journal of Mathematical Education in Science and Technology, 2019

Christopher C. Tisdell

By using the method of reduction of order and the differential equation (1), they obtain the forms and Letting the differential equation of interest at hand now becomes Wilmer III and Costa [7, p.241] then introduce a sequence of recusively defined functions in the following form: Wilmer III and Costa go on to construct the expression Finally, Wilmer III and Costa verify that their constructed expression (7) satisfies (4). This involves differentiating both sides of (7) with respect to x twice under the assumption that the summation and differentiation order can be interchanged.

Reduction of order

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Higher-Order Linear Equations and the Reduction of Order Method

Pedogogical perspectives on the method of Wilmer III and Costa for solving second-order differential equations