59.1.630 problem 647

Internal problem ID [9802]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 647
Date solved : Monday, January 27, 2025 at 06:14:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.203 (sec). Leaf size: 43

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

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