59.1.743 problem 763

Internal problem ID [9915]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 763
Date solved : Monday, January 27, 2025 at 06:15:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

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

\[ y = c_{1} x +c_{2} {\mathrm e}^{-x} \left (x +4\right ) \]

✓ Solution by Mathematica

Time used: 0.334 (sec). Leaf size: 96

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

\[ y(x)\to \frac {2 i \left ((c_1 (x+2)+2 i c_2) \cosh \left (\frac {x+2}{2}\right )-(i c_2 (x+2)+2 c_1) \sinh \left (\frac {x+2}{2}\right )\right ) \exp \left (\int _1^x\frac {1-K[1]}{2 K[1]+4}dK[1]\right )}{\sqrt {\pi } (-i (x+2))^{3/2}} \]