23.1.669 problem 664

Internal problem ID [5276]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 664
Date solved : Tuesday, September 30, 2025 at 12:06:37 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.305 (sec). Leaf size: 46

ode:=x*(3*x-7*y(x)^2)*diff(y(x),x)+(5*x-3*y(x)^2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (x \right )-c_1 +\frac {4 \ln \left (\frac {y-\sqrt {x}}{\sqrt {x}}\right )}{13}+\frac {4 \ln \left (\frac {y+\sqrt {x}}{\sqrt {x}}\right )}{13}+\frac {6 \ln \left (\frac {y}{\sqrt {x}}\right )}{13} = 0 \]

✓ Mathematica. Time used: 3.777 (sec). Leaf size: 288

ode=x(3 x-7 y[x]^2)D[y[x],x]+(5  x-3 y[x]^2)y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,1\right ]\\ y(x)&\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,2\right ]\\ y(x)&\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,3\right ]\\ y(x)&\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,4\right ]\\ y(x)&\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,5\right ]\\ y(x)&\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,6\right ]\\ y(x)&\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,7\right ] \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(3*x - 7*y(x)**2)*Derivative(y(x), x) + (5*x - 3*y(x)**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-5*x + 3*y(x)**2)*y(x)/(x*(3*x - 7*y(x)**