59.1.220 problem 223

Internal problem ID [9392]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 223
Date solved : Sunday, March 30, 2025 at 02:33:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 42

ode:=diff(diff(y(x),x),x)+x*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\left (x -1\right ) \left (x +1\right ) \left (c_1 \sqrt {2}\, \sqrt {\pi }\, \operatorname {erfi}\left (\frac {\sqrt {2}\, x}{2}\right )-c_2 \right ) {\mathrm e}^{-\frac {x^{2}}{2}}+2 c_1 x \]

✓ Mathematica. Time used: 0.201 (sec). Leaf size: 52

ode=D[y[x],{x,2}]+x*D[y[x],x]+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-\frac {x^2}{2}} \left (x^2-1\right ) \left (c_2 \int _1^x\frac {e^{\frac {K[1]^2}{2}}}{\left (K[1]^2-1\right )^2}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + 3*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False