7.8.17 problem 17

Internal problem ID [231]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 17
Date solved : Tuesday, March 04, 2025 at 11:05:50 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=diff(y(x),x)+y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{x +c_1} \]

✓ Mathematica. Time used: 0.095 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = \frac {1}{C_{1} + x} \]