59.1.663 problem 680

Internal problem ID [9835]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 680
Date solved : Monday, January 27, 2025 at 06:14:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x^{2} 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^2*diff(y(x),x)-(2+x)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 40

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

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