78.10.10 problem 11 (b)

Internal problem ID [18200]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 11 (b)
Date solved : Monday, March 31, 2025 at 05:22:36 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*}

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

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

\[ y = {\mathrm e}^{-\frac {x^{2}}{2}} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 77

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

\[ y(x)\to \frac {1}{2} e^{-x} \left (2 c_1 e^{-\frac {i x^2}{2}} \operatorname {HermiteH}\left (-\frac {1}{2},\sqrt [4]{-1} x\right )+\sqrt {2} c_2 \sqrt [4]{i x^2} \operatorname {Gamma}\left (\frac {3}{4}\right ) \operatorname {BesselI}\left (-\frac {1}{4},\frac {i x^2}{2}\right )\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) + (x**2 + 1)*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False