10.3.11 problem 15

Internal problem ID [1176]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 15
Date solved : Saturday, March 29, 2025 at 10:44:37 PM
CAS classification : [_quadrature]

\begin{align*} y^{3}+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=y(t)^3+diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {2 t +c_1}} \\ y &= -\frac {1}{\sqrt {2 t +c_1}} \\ \end{align*}

✓ Mathematica. Time used: 0.122 (sec). Leaf size: 40

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

\begin{align*} y(t)\to -\frac {1}{\sqrt {2 t-2 c_1}} \\ y(t)\to \frac {1}{\sqrt {2 t-2 c_1}} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.313 (sec). Leaf size: 39

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

\[ \left [ y{\left (t \right )} = - \frac {\sqrt {2} \sqrt {- \frac {1}{C_{1} - t}}}{2}, \ y{\left (t \right )} = \frac {\sqrt {2} \sqrt {- \frac {1}{C_{1} - t}}}{2}\right ] \]