23.1.310 problem 299 (a)

Internal problem ID [4917]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 299 (a)
Date solved : Tuesday, September 30, 2025 at 08:56:34 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = -\tanh \left (-\operatorname {arctanh}\left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.167 (sec). Leaf size: 56

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) (K[1]+1)}dK[1]\&\right ]\left [\int _1^x\frac {1}{K[2]^2-1}dK[2]+c_1\right ]\\ y(x)&\to -1\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.296 (sec). Leaf size: 19

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

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