72.1.24 problem 27

Internal problem ID [14545]
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 1.2. page 33
Problem number : 27
Date solved : Thursday, March 13, 2025 at 03:33:18 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 9

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

\[ y = \frac {1}{t +2} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 10

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

\[ y(t)\to \frac {1}{t+2} \]

✓ Sympy. Time used: 0.168 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = \frac {1}{t + 2} \]