Abstract
In this chapter, we shall study the following initial value problem for a second order differential equation: Find a function u(x) defined for x ≥ 0 satisfying
where u 0 and u 1 are given initial data. We here require two initial conditions because the problem involves a second order derivative. We may compare with the first order initial value problem: u′(x) = −u(x) for x > 0, u(0) = u 0, with the solution u(x) = exp(−x), which we studied in the previous chapter.
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© 2004 Springer-Verlag Berlin Heidelberg
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Eriksson, K., Estep, D., Johnson, C. (2004). Trigonometric Functions. In: Applied Mathematics: Body and Soul. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05798-8_6
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DOI: https://doi.org/10.1007/978-3-662-05798-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05658-1
Online ISBN: 978-3-662-05798-8
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