60.1.17 problem Problem 17

Internal problem ID [15145]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 17
Date solved : Thursday, October 02, 2025 at 10:04:30 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y^{\prime }&=\frac {y}{y^{3}+x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 224

ode:=diff(y(x),x) = y(x)/(x+y(x)^3); 
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: 1.094 (sec). Leaf size: 263

ode=D[y[x],x]==y[x]/(x+y[x]^3); 
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(Derivative(y(x), x) - y(x)/(x + y(x)**3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out