23.1.300 problem 290

Internal problem ID [4907]
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 : 290
Date solved : Tuesday, September 30, 2025 at 08:56:14 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = x^{2}-2+\frac {c_1}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to x^2+\frac {c_1}{\sqrt {x^2+1}}-2 \end{align*}

✓ Sympy. Time used: 0.240 (sec). Leaf size: 17

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

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