23.2.146 problem 149

Internal problem ID [5501]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 149
Date solved : Tuesday, September 30, 2025 at 12:45:40 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\begin{align*} y &= c_1 x \\ y &= \frac {x +c_1}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to c_1 x\\ y(x)&\to \frac {x+c_1}{x}\\ y(x)&\to 0\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 12

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

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