59.1.320 problem 327

Internal problem ID [9492]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 327
Date solved : Monday, January 27, 2025 at 06:03:25 PM
CAS classification : [_Laguerre]

\begin{align*} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 24

dsolve(2*x*diff(y(x),x$2)-(3+2*x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {7}{2}\right ], x\right ) x^{{5}/{2}}-\frac {2 c_{2} \left (x -\frac {3}{2}\right ) {\mathrm e}^{x}}{3} \]

✓ Solution by Mathematica

Time used: 0.900 (sec). Leaf size: 52

DSolve[2*x*D[y[x],{x,2}]-(3+2*x)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^x (2 x-3) \left (c_2 \int _1^x\frac {4 e^{-K[1]} K[1]^{3/2}}{(3-2 K[1])^2}dK[1]+c_1\right ) \]