76.3.17 problem 17

Internal problem ID [17317]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 17
Date solved : Monday, March 31, 2025 at 03:52:16 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=y_{0} \end{align*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 16

ode:=diff(y(t),t)+y(t)^3 = 0; 
ic:=y(0) = y__0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {y_{0}}{\sqrt {2 t \,y_{0}^{2}+1}} \]

✓ Mathematica. Time used: 0.14 (sec). Leaf size: 33

ode=D[y[t],t]+y[t]^3==0; 
ic={y[0]==y0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to -\frac {1}{\sqrt {2 t+\frac {1}{\text {y0}^2}}} \\ y(t)\to \frac {1}{\sqrt {2 t+\frac {1}{\text {y0}^2}}} \\ \end{align*}

✓ Sympy. Time used: 0.411 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)**3 + Derivative(y(t), t),0) 
ics = {y(0): y__0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {\sqrt {2} \sqrt {- \frac {1}{- t - \frac {1}{2 \left (y^{0}\right )^{2}}}}}{2} \]