7.17.1 problem 1

Internal problem ID [514]
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 : 1
Date solved : Monday, January 27, 2025 at 02:54:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 20

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

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