80.2.1 problem 1

Internal problem ID [21144]
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 2. Theory of first order differential equations. Excercise 2.6 at page 37
Problem number : 1
Date solved : Thursday, October 02, 2025 at 07:09:53 PM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.135 (sec). Leaf size: 35

ode:=diff(x(t),t) = t+x(t)^2; 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \frac {\sqrt {3}\, \operatorname {AiryAi}\left (1, -t \right )+\operatorname {AiryBi}\left (1, -t \right )}{\sqrt {3}\, \operatorname {AiryAi}\left (-t \right )+\operatorname {AiryBi}\left (-t \right )} \]

✓ Mathematica. Time used: 0.865 (sec). Leaf size: 80

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

\begin{align*} x(t)&\to -\frac {t^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 t^{3/2}}{3}\right )-t^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2 t^{3/2}}{3}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 t^{3/2}}{3}\right )}{2 t \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 t^{3/2}}{3}\right )} \end{align*}

✗ Sympy

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

TypeError : bad operand type for unary -: list