60.1.287 problem 293

Internal problem ID [10301]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 293
Date solved : Sunday, March 30, 2025 at 03:53:47 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 x y&=0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 35

ode:=x*(y(x)^2-3*x)*diff(y(x),x)+2*y(x)^3-5*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (x \right )-c_1 -\frac {2 \ln \left (\frac {5 y^{2}-13 x}{x}\right )}{65}+\frac {6 \ln \left (\frac {y}{\sqrt {x}}\right )}{13} = 0 \]

✓ Mathematica. Time used: 6.613 (sec). Leaf size: 661

ode=x*(y[x]^2-3*x)*D[y[x],x]+2*y[x]^3-5*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(-3*x + y(x)**2)*Derivative(y(x), x) - 5*x*y(x) + 2*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-5*x + 2*y(x)**2)*y(x)/(x*(3*x - y(x)**2)) cannot be solved by the factorable group method