Internal problem ID [7124]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 399.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)+(x^2+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x^{2}}{2}} c_{1}+c_{2} x \,{\mathrm e}^{-\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 22
DSolve[y''[x]+2*x*y'[x]+(x^2+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {x^2}{2}} (c_2 x+c_1) \\ \end{align*}