59.1.339 problem 346

Internal problem ID [9511]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 346
Date solved : Monday, January 27, 2025 at 06:03:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 19

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

\[ y(x)\to e^{-x} (c_2 \log (x)+c_1) \]