56.5.2 problem 2

Internal problem ID [8963]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:25:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 22

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

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