72.8.20 problem 33

Internal problem ID [14713]
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 : 33
Date solved : Monday, March 31, 2025 at 12:54:57 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.175 (sec). Leaf size: 18

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

\[ y = -\frac {3}{\sqrt {-6 t^{3}-18 t +36}} \]

✓ Mathematica. Time used: 0.185 (sec). Leaf size: 28

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

\[ y(t)\to -\frac {\sqrt {\frac {3}{2}}}{\sqrt {-t^3-3 t+6}} \]

✓ Sympy. Time used: 0.578 (sec). Leaf size: 26

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

\[ y{\left (t \right )} = - \frac {\sqrt {6} \sqrt {- \frac {1}{t^{3} + 3 t - 6}}}{2} \]