59.1.621 problem 638

Internal problem ID [9793]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 638
Date solved : Monday, January 27, 2025 at 06:14:20 PM
CAS classification : [_Laguerre]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 15

dsolve(2*t*diff(y(t),t$2)+(1-2*t)*diff(y(t),t)-y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{t} \left (\operatorname {erf}\left (\sqrt {t}\right ) c_{1} +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 21

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

\[ y(t)\to e^t \left (c_1-c_2 \Gamma \left (\frac {1}{2},t\right )\right ) \]