59.1.250 problem 253

Internal problem ID [9422]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 253
Date solved : Monday, January 27, 2025 at 06:02:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 16

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

\[ y = \frac {c_{1} +c_{2} {\mathrm e}^{-2 x}}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 26

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

\[ y(x)\to \frac {2 c_1 e^{-2 x}+c_2}{2 \sqrt {x}} \]