72.8.2 problem 3

Internal problem ID [14695]
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. Review Exercises for chapter 1. page 136
Problem number : 3
Date solved : Monday, March 31, 2025 at 12:53:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \frac {1}{5} t^{5}+\frac {1}{3} t^{3}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 22

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

\[ y(t)\to \frac {t^5}{5}+\frac {t^3}{3}+c_1 \]

✓ Sympy. Time used: 0.135 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{1} + \frac {t^{5}}{5} + \frac {t^{3}}{3} \]