29.23.8 problem 639

Internal problem ID [5230]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 639
Date solved : Sunday, March 30, 2025 at 07:05:51 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 6.502 (sec). Leaf size: 661

ode=x(3 x-y[x]^2)D[y[x],x]+(5 x-2 y[x]^2)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 - 2*y(x)**2)*y(x),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