59.1.39 problem 41

Internal problem ID [9211]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 41
Date solved : Monday, January 27, 2025 at 05:52:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 19

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

\[ y(x)\to e^{x+1} x (c_2 x+c_1) \]