59.1.438 problem 451

Internal problem ID [9610]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 451
Date solved : Monday, January 27, 2025 at 06:04:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 23

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

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