29.13.18 problem 372

Internal problem ID [4972]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 372
Date solved : Tuesday, March 04, 2025 at 07:39:35 PM
CAS classification : [_separable]

\begin{align*} \left (-x^{4}+1\right ) y^{\prime }&=2 x \left (1-y^{2}\right ) \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 31

ode:=(-x^4+1)*diff(y(x),x) = 2*x*(1-y(x)^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = -\tanh \left (\frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (x +1\right )}{2}-\frac {\ln \left (x^{2}+1\right )}{2}+2 c_{1} \right ) \]

✓ Mathematica. Time used: 0.981 (sec). Leaf size: 55

ode=(1-x^4)D[y[x],x]==2 x(1-y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.523 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*(1 - y(x)**2) + (1 - x**4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} x^{2} - C_{1} + x^{2} + 1}{- C_{1} x^{2} + C_{1} + x^{2} + 1} \]