23.1.70 problem 64

Internal problem ID [4677]
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 : 64
Date solved : Tuesday, September 30, 2025 at 07:58:07 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {3}{-1+3 \,{\mathrm e}^{-\frac {3 x^{2}}{2}} c_1} \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (K[1]+3)}dK[1]\&\right ]\left [\frac {x^2}{2}+c_1\right ]\\ y(x)&\to -3\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 6.593 (sec). Leaf size: 83

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

\[ \left [ y{\left (x \right )} = \frac {3 \left (\sqrt {e^{6 C_{1} + 3 x^{2}}} - e^{6 C_{1} + 3 x^{2}}\right )}{e^{6 C_{1} + 3 x^{2}} - 1}, \ y{\left (x \right )} = - \frac {3 \left (\sqrt {e^{6 C_{1} + 3 x^{2}}} + e^{6 C_{1} + 3 x^{2}}\right )}{e^{6 C_{1} + 3 x^{2}} - 1}\right ] \]