66.2.1 problem 1

Internal problem ID [15923]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:30:08 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \frac {1}{3} t^{3}+\frac {1}{2} t^{2}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.078 (sec). Leaf size: 14

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

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