23.1.9 problem 8

Internal problem ID [4616]
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 : 8
Date solved : Tuesday, September 30, 2025 at 07:37:04 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = x^{2}-2+{\mathrm e}^{-\frac {x^{2}}{2}} c_1 \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.138 (sec). Leaf size: 15

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

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