23.1.390 problem 375

Internal problem ID [4997]
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 : 375
Date solved : Tuesday, September 30, 2025 at 09:13:42 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 31

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

\[ y = -\tanh \left (-\frac {\ln \left (x^{2}+1\right )}{2}+\frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (x +1\right )}{2}+2 c_1 \right ) \]

✓ Mathematica. Time used: 0.204 (sec). Leaf size: 60

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 \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) (K[1]+1)}dK[1]\&\right ]\left [\int _1^x\frac {2 K[2]}{K[2]^4-1}dK[2]+c_1\right ]\\ y(x)&\to -1\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.360 (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)
 

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