Internal problem ID [7486]
Book: Second order enumerated odes
Section: section 2
Problem number: 45.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Bessel]
\[ \boxed {y^{\prime \prime } x^{2}+y^{\prime } x +\left (x^{2}-5\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (\sqrt {5}, x\right )+c_{2} \operatorname {BesselY}\left (\sqrt {5}, x\right ) \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 26
DSolve[x^2*y''[x]+x*y'[x]+(x^2-5)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {BesselJ}\left (\sqrt {5},x\right )+c_2 \operatorname {BesselY}\left (\sqrt {5},x\right ) \]