82.54.7 problem Ex. 7

Internal problem ID [18952]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 7
Date solved : Monday, March 31, 2025 at 06:26:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 44

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

\[ y(x)\to \frac {1}{4} e^{-x \left (x+\sqrt {2}\right )} \left (\sqrt {2} c_2 e^{2 \sqrt {2} x}+4 c_1\right ) \]

✗ Sympy

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

False