80.1.9 problem 9

Internal problem ID [21127]
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 1. First order linear differential equations. Excercise 1.5 at page 13
Problem number : 9
Date solved : Thursday, October 02, 2025 at 07:09:31 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 12

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

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