15.20.12 problem 12

Internal problem ID [3320]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 12
Date solved : Tuesday, March 04, 2025 at 04:34:49 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}+y^{\prime } x y&=2 y^{2} \end{align*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 28

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

\begin{align*} y \left (x \right ) &= -\frac {x^{3}}{27} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (c_{1} x +1\right )^{2}}{4 c_{1}^{3}} \\ \end{align*}

✓ Mathematica. Time used: 121.636 (sec). Leaf size: 10682

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

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✗ Sympy

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

Timed Out