23.1.587 problem 580

Internal problem ID [5194]
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 : 580
Date solved : Tuesday, September 30, 2025 at 11:52:07 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (1+2 x y\right ) y^{\prime }+\left (2+3 x y\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 45

ode:=x*(1+2*x*y(x))*diff(y(x),x)+(2+3*x*y(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-x +\sqrt {x \left (4 c_1 +x \right )}}{2 x^{2}} \\ y &= \frac {-x -\sqrt {x \left (4 c_1 +x \right )}}{2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.436 (sec). Leaf size: 69

ode=x*(1+2*x*y[x])*D[y[x],x]+(2+3*x*y[x])*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}}\\ y(x)&\to \frac {-x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}} \end{align*}

✓ Sympy. Time used: 0.611 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(2*x*y(x) + 1)*Derivative(y(x), x) + (3*x*y(x) + 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {- \sqrt {\frac {C_{1}}{x} + 1} - 1}{2 x}, \ y{\left (x \right )} = \frac {\sqrt {\frac {C_{1}}{x} + 1} - 1}{2 x}\right ] \]