23.2.144 problem 147

Internal problem ID [5499]
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 : 147
Date solved : Tuesday, September 30, 2025 at 12:45:38 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.162 (sec). Leaf size: 17

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

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