7.3.29 problem 29

Internal problem ID [69]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 29
Date solved : Tuesday, March 04, 2025 at 10:41:36 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 17

ode:=diff(y(x),x) = y(x)^2; 
ic:=y(a) = b; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {b}{1+\left (a -x \right ) b} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 18

ode=D[y[x],x]== y[x]^2; 
ic={y[a]==b}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {b}{a b-b x+1} \]

✓ Sympy. Time used: 0.158 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = - \frac {1}{x + \frac {- a b - 1}{b}} \]