The first-order differential equation dy/dx = i2 + y 2 cannot be solved in terms of
Chapter 5, Problem 22(choose chapter or problem)
The first-order differential equation dy/dx = i2 + y 2 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 = _ _!_ d dx u leads to the equation u" + i2u = 0. u (b) Use (18) in Section 5.3 to find the general solution of u" + i2u = 0. (c) Use (20) and (21) in Section 5.3 in the forms J(x) = 11_ lv(x) - Iv+ 1(x) x and J(x) = _11_ lv(x) + lv1(x) x as an aid in showing that a one-parameter family of solutions of dyldx = i2 + y 2 is given by
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