11.1.1 problem 1.1-2 (a)

Internal problem ID [3418]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-2, page 6
Problem number : 1.1-2 (a)
Date solved : Tuesday, September 30, 2025 at 06:37:55 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=t^{2}+3 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(t),t) = t^2+3; 
dsolve(ode,y(t), singsol=all);
 

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

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

ode=D[y[t],t]==t^2+3; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.072 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2 + Derivative(y(t), t) - 3,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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