18.1.9 problem Problem 14.5 (c)

Internal problem ID [3465]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.5 (c)
Date solved : Sunday, March 30, 2025 at 01:43:19 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 220

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

\begin{align*} y &= \frac {\left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}-6 c_1}{3 \left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ y &= -\frac {i \left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+6 i \sqrt {3}\, c_1 +\left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}-6 c_1}{6 \left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ y &= \frac {i \left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+6 i \sqrt {3}\, c_1 -\left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}+6 c_1}{6 \left (27 x +3 \sqrt {24 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 1.697 (sec). Leaf size: 263

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

\begin{align*} y(x)\to \frac {2\ 3^{2/3} c_1-\sqrt [3]{3} \left (-9 x+\sqrt {81 x^2+24 c_1{}^3}\right ){}^{2/3}}{3 \sqrt [3]{-9 x+\sqrt {81 x^2+24 c_1{}^3}}} \\ y(x)\to \frac {\sqrt [3]{3} \left (1-i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+24 c_1{}^3}\right ){}^{2/3}-2 \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) c_1}{6 \sqrt [3]{-9 x+\sqrt {81 x^2+24 c_1{}^3}}} \\ y(x)\to \frac {\sqrt [3]{3} \left (1+i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+24 c_1{}^3}\right ){}^{2/3}-2 \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) c_1}{6 \sqrt [3]{-9 x+\sqrt {81 x^2+24 c_1{}^3}}} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out