58.21.3 problem 5

Internal problem ID [14945]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.6, Exercises page 567
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:56:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=(t^3-2*t^2)*diff(diff(x(t),t),t)-(t^3+2*t^2-6*t)*diff(x(t),t)+(3*t^2-6)*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,t^{3}+c_2 t \,{\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 19

ode=(t^3-2*t^2)*D[x[t],{t,2}]-(t^3+2*t^2-6*t)*D[x[t],t]+(3*t^2-6)*x[t]==0; 
ic={}; 
DSolve[{ode,ic},{x[t]},t,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((3*t**2 - 6)*x(t) + (t**3 - 2*t**2)*Derivative(x(t), (t, 2)) - (t**3 + 2*t**2 - 6*t)*Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

False