Internal problem ID [7038]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 307.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 23
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)
\[ y \relax (x ) = {\mathrm e}^{-x^{2}} c_{1}+c_{2} {\mathrm e}^{-x^{2}} \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 21
DSolve[x*y''[x]+(4*x^2+1)*y'[x]+4*x*(x^2+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x^2} (c_2 \log (x)+c_1) \\ \end{align*}