69.12.36 problem 310

Internal problem ID [18189]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 310
Date solved : Thursday, October 02, 2025 at 03:08:43 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: 0.010 (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: 0.395 (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: 0.674 (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)
 

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