77.1.142 problem thm 19 (page 244)

Internal problem ID [18032]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : thm 19 (page 244)
Date solved : Tuesday, January 28, 2025 at 11:23:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 36

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

\[ y(x)\to x \left (c_1 \operatorname {BesselJ}\left (\sqrt {m^2+1},x\right )+c_2 \operatorname {BesselY}\left (\sqrt {m^2+1},x\right )\right ) \]