72.2.19 problem 16 (iv)

Internal problem ID [14575]
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 (iv)
Date solved : Thursday, March 13, 2025 at 03:36:24 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (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]==2-t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.130 (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)
 

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