85.24.2 problem 2

Internal problem ID [22579]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 57
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:52:09 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y+\left (y^{3}-x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 224

ode:=y(x)+(y(x)^3-x)*diff(y(x),x) = 0; 
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: 1.144 (sec). Leaf size: 259

ode=y[x]+(y[x]^3-x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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