89.5.19 problem 19

Internal problem ID [24369]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 19
Date solved : Thursday, October 02, 2025 at 10:22:22 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {(x+1) (x-2 \log (x+1)-c_1)}{x-1} \end{align*}

✓ Sympy. Time used: 0.211 (sec). Leaf size: 31

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

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