78.12.34 problem 7 (a)

Internal problem ID [18250]
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 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 7 (a)
Date solved : Monday, March 31, 2025 at 05:23:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 34

ode:=x*diff(diff(y(x),x),x)+(x^2-1)*diff(y(x),x)+x^3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x^{2}}{4}} \left (c_1 \cos \left (\frac {x^{2} \sqrt {3}}{4}\right )+c_2 \sin \left (\frac {x^{2} \sqrt {3}}{4}\right )\right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 48

ode=x*D[y[x],{x,2}] +(x^2-1)*D[y[x],x]+x^3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-\frac {x^2}{4}} \left (c_2 \cos \left (\frac {\sqrt {3} x^2}{4}\right )+c_1 \sin \left (\frac {\sqrt {3} x^2}{4}\right )\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*y(x) + x*Derivative(y(x), (x, 2)) + (x**2 - 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False