Concept explainers
The first-order differential equation dy/dx = x2 + y2 cannot be solved in terms of elementary functions. However, a solution can be expressed in terms of Bessel functions.
(a) Show that the substitution
(b) Use (20) in Section 6.4 to find the general solution of u″ + x2u = 0.
(c) Use (22) and (23) in Section 6.4 in the forms
and
as an aid to show that a one-parameter family of solutions of dy/dx = x2 + y2 is given by
Although we shall not supply the details, the general solution of (20).
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,