90.7.4 problem 4

Internal problem ID [25158]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 99
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:55:31 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 11

ode:=diff(y(t),t) = t^2+1; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

ode=D[y[t],t]== 1+t^2; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.066 (sec). Leaf size: 8

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

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