59.1.217 problem 220

Internal problem ID [9389]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 220
Date solved : Monday, January 27, 2025 at 06:02:13 PM
CAS classification : [_Lienard]

\begin{align*} z y^{\prime \prime }-2 y^{\prime }+z y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 23

dsolve(z*diff(y(z),z$2)-2*diff(y(z),z)+z*y(z)=0,y(z), singsol=all)
 

\[ y \left (z \right ) = \left (c_{1} z +c_{2} \right ) \cos \left (z \right )+\sin \left (z \right ) \left (c_{2} z -c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 39

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

\[ y(z)\to -\sqrt {\frac {2}{\pi }} ((c_1 z+c_2) \cos (z)+(c_2 z-c_1) \sin (z)) \]