59.1.490 problem 506

Internal problem ID [9662]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 506
Date solved : Monday, January 27, 2025 at 06:12:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 59

dsolve((2+x)*diff(y(x),x$2)+(1+x)*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y = x c_{2} {\mathrm e}^{-x -2} \left (x -4\right ) \left (x +2\right )^{2} \operatorname {Ei}_{1}\left (-x -2\right )+c_{1} {\mathrm e}^{-x} x \left (x -4\right ) \left (x +2\right )^{2}+c_{2} \left (x^{3}-x^{2}-10 x -6\right ) \]

✓ Solution by Mathematica

Time used: 0.496 (sec). Leaf size: 106

DSolve[(2+x)*D[y[x],{x,2}]+(1+x)*D[y[x],x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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