59.1.442 problem 455

Internal problem ID [9614]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 455
Date solved : Monday, January 27, 2025 at 06:04:40 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

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

\[ y(x)\to x (c_2 x+c_1) \]