23.1.303 problem 293

Internal problem ID [4910]
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 : 293
Date solved : Tuesday, September 30, 2025 at 08:56:20 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \left (x^{2}+c_1 \right ) \left (x^{2}+1\right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \left (x^2+1\right ) \left (x^2+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} x^{2} + C_{1} + x^{4} + x^{2} \]