78.12.35 problem 7 (b)

Internal problem ID [18243]
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 (b)
Date solved : Friday, March 14, 2025 at 12:42:09 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 x y^{\prime }+x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 56

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

\[ y = {\mathrm e}^{-\frac {x^{2} \left (3+\sqrt {5}\right )}{4}} x \left (\operatorname {KummerM}\left (\frac {3}{4}+\frac {3 \sqrt {5}}{20}, \frac {3}{2}, \frac {\sqrt {5}\, x^{2}}{2}\right ) c_{1} +\operatorname {KummerU}\left (\frac {3}{4}+\frac {3 \sqrt {5}}{20}, \frac {3}{2}, \frac {\sqrt {5}\, x^{2}}{2}\right ) c_{2} \right ) \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 84

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

\[ y(x)\to e^{-\frac {1}{4} \left (3+\sqrt {5}\right ) x^2} \left (c_1 \operatorname {HermiteH}\left (\frac {1}{10} \left (-5-3 \sqrt {5}\right ),\frac {\sqrt [4]{5} x}{\sqrt {2}}\right )+c_2 \operatorname {Hypergeometric1F1}\left (\frac {1}{20} \left (5+3 \sqrt {5}\right ),\frac {1}{2},\frac {\sqrt {5} x^2}{2}\right )\right ) \]

✗ Sympy

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

False