77.1.144 problem 170 (page 245)

Internal problem ID [18034]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 170 (page 245)
Date solved : Tuesday, January 28, 2025 at 11:23:11 AM
CAS classification : [_Lienard]

\begin{align*} y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+2*p/x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]+2*p/x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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