71.1.9 problem 20 (page 30)

Internal problem ID [19185]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 20 (page 30)
Date solved : Thursday, October 02, 2025 at 03:41:21 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 17

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

\[ y = -x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_1}}{x}\right ) \]

✓ Mathematica. Time used: 0.254 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to -x W\left (-\frac {e^{-c_1}}{x}\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.279 (sec). Leaf size: 10

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

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