72.2.23 problem 16 (viii)

Internal problem ID [14579]
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 : 16 (viii)
Date solved : Thursday, March 13, 2025 at 03:36:32 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

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

\[ y(t)\to \frac {t^3}{3}-2 t+c_1 \]

✓ Sympy. Time used: 0.127 (sec). Leaf size: 12

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

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