61.2.1 problem Problem 1(a)

Internal problem ID [15239]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(a)
Date solved : Thursday, October 02, 2025 at 10:07:50 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }+x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

\[ y = \left (\operatorname {BesselY}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_2 +\operatorname {BesselJ}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_1 \right ) \sqrt {x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to c_2 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},(-1+i) x\right )+c_1 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},(1+i) x\right ) \end{align*}

✗ Sympy

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

False