59.1.394 problem 406

Internal problem ID [9566]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 406
Date solved : Monday, January 27, 2025 at 06:04:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 17

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

\[ y(x)\to e x \left (c_2 e^x+c_1\right ) \]