59.1.251 problem 254

Internal problem ID [9423]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 254
Date solved : Monday, January 27, 2025 at 06:02:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

dsolve(x^2*diff(y(x),x$2)+x*(4+x)*diff(y(x),x)+(2+x)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.218 (sec). Leaf size: 36

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

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