7.17.7 problem 7

Internal problem ID [520]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:54:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+(1+x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\operatorname {BesselY}\left (0, x\right ) c_2 +\operatorname {BesselJ}\left (0, x\right ) c_1}{x} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+(1+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \operatorname {BesselJ}(0,x)+c_2 \operatorname {BesselY}(0,x)}{x} \]