63.1.60 problem 79

Internal problem ID [15500]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 79
Date solved : Thursday, October 02, 2025 at 10:19:01 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \frac {x}{c_1 x +1} \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.088 (sec). Leaf size: 10

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

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