80.3.53 problem 56(a)

Internal problem ID [21217]
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 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 56(a)
Date solved : Thursday, October 02, 2025 at 07:26:58 PM
CAS classification : [_linear]

\begin{align*} x&=t \left (1+x^{\prime }\right )+x^{\prime } \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=x(t) = t*(1+diff(x(t),t))+diff(x(t),t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \left (-t -1\right ) \ln \left (t +1\right )-1+\left (t +1\right ) c_1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 22

ode=x[t]==t*(1+D[x[t],t])+D[x[t],t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -(t+1) \log (t+1)+c_1 (t+1)-1 \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t*(Derivative(x(t), t) + 1) + x(t) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} t - C_{1} - t \log {\left (t - 1 \right )} + \log {\left (t - 1 \right )} + 1 \]