23.2.273 problem 290

Internal problem ID [5628]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 290
Date solved : Tuesday, September 30, 2025 at 01:15:45 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.105 (sec). Leaf size: 33

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

\begin{align*} y &= \frac {a \,x^{3}}{27} \\ y &= 0 \\ y &= \frac {\left (x a c_1 -1\right )^{2}}{4 c_1^{3} a^{2}} \\ \end{align*}

✓ Mathematica. Time used: 86.338 (sec). Leaf size: 13193

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

Too large to display

✗ Sympy

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

Timed Out