72.8.32 problem 47

Internal problem ID [14717]
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 : 47
Date solved : Thursday, March 13, 2025 at 04:16:20 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.072 (sec). Leaf size: 14

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

\[ y = \sqrt {3}\, \tanh \left (\sqrt {3}\, t \right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 37

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

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

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants