59.1.304 problem 307

Internal problem ID [9476]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 307
Date solved : Monday, January 27, 2025 at 06:03:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 21

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

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