The first-order differential equation dy dx x2 y2 cannot be solved in terms of
Chapter 6, Problem 22(choose chapter or problem)
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 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 and J (x) x J(x) J1(x) J
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