59.1.452 problem 466

Internal problem ID [9624]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 466
Date solved : Monday, January 27, 2025 at 06:04:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 15

dsolve(4*x^2*diff(y(x),x$2)+(4*x-8*x^2)*diff(y(x),x)+(4*x^2-4*x-1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 21

DSolve[4*x^2*D[y[x],{x,2}]+(4*x-8*x^2)*D[y[x],x]+(4*x^2-4*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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