77.1.39 problem 56 (page 103)

Internal problem ID [17858]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 56 (page 103)
Date solved : Monday, March 31, 2025 at 04:37:14 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 28

ode:=y(x)^3+2*(x^2-x*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\frac {c_1}{2}}}{\sqrt {-\frac {{\mathrm e}^{c_1}}{x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{c_1}}{x}\right )}}} \]

✓ Mathematica. Time used: 2.854 (sec). Leaf size: 60

ode=y[x]^3+2*(x^2-x*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.061 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x**2 - 2*x*y(x)**2)*Derivative(y(x), x) + y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{- \frac {C_{1}}{2} - \frac {W\left (- \frac {e^{- C_{1}}}{x}\right )}{2}} \]