2.45 problem 45

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]

\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y=0} \]

Solution by Maple

Time used: 0.0 (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]
                                                                                    
                                                                                    
 

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