59.1.818 problem 841

Internal problem ID [9990]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 841
Date solved : Monday, January 27, 2025 at 06:16:30 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(diff(y(x),x),x)+(-8*x^2+4*x)*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: 0.042 (sec). Leaf size: 21

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

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