89.1.11 problem 11

Internal problem ID [24246]
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 21
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:01:32 PM
CAS classification : [_separable]

\begin{align*} x^{2}+y \left (x -1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

ode:=x^2+y(x)*(x-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {-x^{2}-2 \ln \left (x -1\right )+c_1 -2 x} \\ y &= -\sqrt {-x^{2}-2 \ln \left (x -1\right )+c_1 -2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 59

ode=(x^2)+y[x]*(x-1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-x^2-2 x-2 \log (x-1)+3+2 c_1}\\ y(x)&\to \sqrt {-x^2-2 x-2 \log (x-1)+3+2 c_1} \end{align*}

✓ Sympy. Time used: 0.307 (sec). Leaf size: 42

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

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