23.1.302 problem 292

Internal problem ID [4909]
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 : 292
Date solved : Tuesday, September 30, 2025 at 08:56:19 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = \frac {2 x^{3}+3 c_1}{3 x^{2}+3} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {2 x^3+3 c_1}{3 x^2+3} \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {2 x^{3}}{3}}{x^{2} + 1} \]