29.11.5 problem 296

Internal problem ID [4896]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 296
Date solved : Sunday, March 30, 2025 at 04:09:29 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: 0.699 (sec). Leaf size: 47

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 -\frac {x+e^{2 c_1} (x-1)+1}{-x+e^{2 c_1} (x-1)-1} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.478 (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)
 

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