69.1.56 problem 75

Internal problem ID [14138]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 75
Date solved : Monday, March 31, 2025 at 12:10:19 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 37

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-\ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+c_1 \,{\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x +\ln \left (x \right ) x -c_1 x -\textit {\_Z} x \right )} \]

✓ Mathematica. Time used: 0.408 (sec). Leaf size: 38

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (1-\frac {1}{K[1]}\right )dK[1]+\frac {y(x)^2}{x-y(x)}+\log (x)=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out