58.2.45 problem 45

Internal problem ID [9168]
Book : Second order enumerated odes
Section : section 2
Problem number : 45
Date solved : Monday, January 27, 2025 at 05:51:36 PM
CAS classification : [_Bessel]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-5)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {BesselJ}\left (\sqrt {5}, x\right )+c_{2} \operatorname {BesselY}\left (\sqrt {5}, x\right ) \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(x^2-5)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}\left (\sqrt {5},x\right )+c_2 \operatorname {BesselY}\left (\sqrt {5},x\right ) \]