53.1.79 problem 81

Internal problem ID [10551]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 81
Date solved : Tuesday, September 30, 2025 at 07:29:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+(2*x^2+4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x^{2}} \left (c_2 \,\operatorname {erf}\left (\frac {i \sqrt {3}\, x}{2}\right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 42

ode=2*D[y[x],{x,2}]+5*x*D[y[x],x]+(4+2*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} e^{-x^2} \left (\sqrt {3 \pi } c_2 \text {erfi}\left (\frac {\sqrt {3} x}{2}\right )+3 c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x*Derivative(y(x), x) + (2*x**2 + 4)*y(x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False