59.1.466 problem 481

Internal problem ID [9638]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 481
Date solved : Monday, January 27, 2025 at 06:04:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 72

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

\[ y = {\mathrm e}^{-x -2} c_{2} \left (x^{2}-6 x +4\right ) \left (x +2\right )^{3} \operatorname {Ei}_{1}\left (-x -2\right )+c_{1} {\mathrm e}^{-x} \left (x^{2}-6 x +4\right ) \left (x +2\right )^{3}+c_{2} \left (x^{4}-x^{3}-18 x^{2}-22 x +8\right ) \]

✓ Solution by Mathematica

Time used: 0.493 (sec). Leaf size: 106

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

\[ y(x)\to \left (x^2-6 x+4\right ) \exp \left (\int _1^x\left (\frac {2}{K[1]+2}-\frac {1}{2}\right )dK[1]-\frac {1}{2} \int _1^x\frac {K[2]}{K[2]+2}dK[2]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[3]}\left (\frac {2}{K[1]+2}-\frac {1}{2}\right )dK[1]\right )}{\left (K[3]^2-6 K[3]+4\right )^2}dK[3]+c_1\right ) \]