59.1.208 problem 211

Internal problem ID [9380]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 211
Date solved : Monday, January 27, 2025 at 06:02:07 PM
CAS classification : [_Laguerre]

\begin{align*} t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(t*diff(y(t),t$2)-(4+t)*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
 

\[ y = c_{1} \left (t^{2}+6 t +12\right )+c_{2} {\mathrm e}^{t} \left (t^{2}-6 t +12\right ) \]

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 87

DSolve[t*D[y[t],{t,2}]-(4+t)*D[y[t],t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2 e^{\frac {t+5}{2}} \sqrt {t} \left (\left (c_2 t^2-6 i c_1 t+12 c_2\right ) \cosh \left (\frac {t}{2}\right )+i \left (c_1 \left (t^2+12\right )+6 i c_2 t\right ) \sinh \left (\frac {t}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i t}} \]