64.6.2 problem 2

Internal problem ID [13281]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 2
Date solved : Monday, March 31, 2025 at 07:45:08 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational]

\begin{align*} \left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 1127

ode:=(3*x^2*y(x)^2-x)*diff(y(x),x)+2*x*y(x)^3-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 34.443 (sec). Leaf size: 356

ode=(3*x^2*y[x]^2-x)*D[y[x],x]+(2*x*y[x]^3-y[x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {2 \sqrt [3]{3} x^3+\sqrt [3]{2} \left (\sqrt {3} \sqrt {x^8 \left (-4 x+27 c_1{}^2\right )}+9 c_1 x^4\right ){}^{2/3}}{6^{2/3} x^2 \sqrt [3]{\sqrt {3} \sqrt {x^8 \left (-4 x+27 c_1{}^2\right )}+9 c_1 x^4}} \\ y(x)\to \frac {i \sqrt [3]{3} \left (\sqrt {3}+i\right ) \left (2 \sqrt {3} \sqrt {x^8 \left (-4 x+27 c_1{}^2\right )}+18 c_1 x^4\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) x^3}{12 x^2 \sqrt [3]{\sqrt {3} \sqrt {x^8 \left (-4 x+27 c_1{}^2\right )}+9 c_1 x^4}} \\ y(x)\to \frac {\sqrt [3]{3} \left (-1-i \sqrt {3}\right ) \left (2 \sqrt {3} \sqrt {x^8 \left (-4 x+27 c_1{}^2\right )}+18 c_1 x^4\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) x^3}{12 x^2 \sqrt [3]{\sqrt {3} \sqrt {x^8 \left (-4 x+27 c_1{}^2\right )}+9 c_1 x^4}} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**3 + (3*x**2*y(x)**2 - x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out