23.1.615 problem 609

Internal problem ID [5222]
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 : 609
Date solved : Tuesday, September 30, 2025 at 11:56:20 AM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 36

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

\[ \frac {{\mathrm e}^{-2 i y} \left (i x +y\right )+2 \left (i y+x \right ) c_1}{2 i y+2 x} = 0 \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 91

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {x}{x^2+K[2]^2}-\int _1^x\left (\frac {2 K[2]^2}{\left (K[1]^2+K[2]^2\right )^2}-\frac {1}{K[1]^2+K[2]^2}\right )dK[1]+1\right )dK[2]+\int _1^x-\frac {y(x)}{K[1]^2+y(x)^2}dK[1]=c_1,y(x)\right ] \]

✗ Sympy

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

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