Internal problem ID [6730]
Book: Second order enumerated odes
Section: section 2
Problem number: 45.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Bessel]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = c_{1} \BesselJ \left (\sqrt {5}, x\right )+c_{2} \BesselY \left (\sqrt {5}, x\right ) \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 26
DSolve[x^2*y''[x]+x*y'[x]+(x^2-5)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 J_{\sqrt {5}}(x)+c_2 Y_{\sqrt {5}}(x) \\ \end{align*}