The first-order differential equation dy/dx = x 2 + y 2 cannot be solved in terms of
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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 y = -1/u du/dx leads to the equation u'' + x2u = 0.
(b) Use (18) in Section 6.4 to find the general solution of u'' + x2u = 0.
(c) Use (20) and (21) in Section 6.4 in the forms
as an aid to show that a one-parameter family of solutions of dy/dx = x2 + y2 is given by
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ANSWER a To show that the substitution y 1u dudx leads to the equation u x2u 0 we need to differenti...View the full answer
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Related Book For 
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill
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