23.3.247 problem 249

Internal problem ID [5961]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 249
Date solved : Tuesday, September 30, 2025 at 02:06:59 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }&=12 y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x) = 12*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,x^{7}+c_1}{x^{3}} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}] == 12*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 x^7+c_1}{x^3} \end{align*}

✓ Sympy. Time used: 0.026 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{3}} + C_{2} x^{4} \]