73.1.26 problem 6

Internal problem ID [19799]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 6
Date solved : Thursday, October 02, 2025 at 04:43:55 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} x^{\prime \prime }-6 x^{\prime } t +12 x&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=t^2*diff(diff(x(t),t),t)-6*t*diff(x(t),t)+12*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = t^{3} \left (c_2 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 16

ode=t^2*D[x[t],{t,2}]-6*t*D[x[t],t]+12*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.091 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t**2*Derivative(x(t), (t, 2)) - 6*t*Derivative(x(t), t) + 12*x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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