87.2.11 problem 12

Internal problem ID [23246]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 17
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:26:48 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y^{2}&=1 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

ode:=x*diff(y(x),x)+y(x)^2 = 1; 
ic:=[y(-2) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 1 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=x*D[y[x],x]+y[x]^2==1; 
ic={y[-2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.195 (sec). Leaf size: 3

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

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