80.5.68 problem D 19

Internal problem ID [21289]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 5. Second order equations. Excercise 5.9 at page 119
Problem number : D 19
Date solved : Thursday, October 02, 2025 at 07:27:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} x^{\prime \prime }+3 x^{\prime } t -3 x&=t^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

\[ x = t c_2 +\frac {c_1}{t^{3}}+\frac {t^{2}}{5} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

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

\begin{align*} x(t)&\to \frac {c_1}{t^3}+\frac {t^2}{5}+c_2 t \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 15

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

\[ x{\left (t \right )} = \frac {C_{1}}{t^{3}} + C_{2} t + \frac {t^{2}}{5} \]