72.3.10 problem 10

Internal problem ID [14603]
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 1.4 page 61
Problem number : 10
Date solved : Monday, March 31, 2025 at 12:40:11 PM
CAS classification : [_Abel]

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

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {1}{2}} \end{align*}

✗ Maple

ode:=diff(y(t),t) = 2*y(t)^3+t^2; 
ic:=y(0) = -1/2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],t]==2*y[t]^3+t^2; 
ic={y[0]==-1/2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2 - 2*y(t)**3 + Derivative(y(t), t),0) 
ics = {y(0): -1/2} 
dsolve(ode,func=y(t),ics=ics)
 

IndexError : Index out of range: a[1]