66.2.2 problem 2

Internal problem ID [15924]
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 : 2
Date solved : Thursday, October 02, 2025 at 10:30:09 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=t^{2}+1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(y(t),t) = t^2+1; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 16

ode=D[y[t],t]==t^2+1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.065 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2 + Derivative(y(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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