85.67.8 problem 8

Internal problem ID [22899]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:16:25 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 16

ode:=x^2*diff(diff(y(x),x),x)-6*y(x) = 0; 
ic:=[y(1) = 2, D(y)(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {4 x^{5}+6}{5 x^{2}} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 19

ode=x^2*D[y[x],{x,2}]-6*y[x]==0; 
ic={y[1]==2,Derivative[1][y][1] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {4 x^5+6}{5 x^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 4)) - 6*y(x),0) 
ics = {y(1): 2, Subs(Derivative(y(x), x), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve x**2*Derivative(y(x), (x, 4)) - 6*y(x)