64.7.6 problem 6

Internal problem ID [13309]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 6
Date solved : Monday, March 31, 2025 at 07:50:37 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.250 (sec). Leaf size: 34

ode:=8*x^2*y(x)^3-2*y(x)^4+(5*x^3*y(x)^2-8*x*y(x)^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \operatorname {RootOf}\left (x^{6} \textit {\_Z}^{48}-x^{6} \textit {\_Z}^{30}-c_1 \right )^{18} x^{2} \\ \end{align*}

✓ Mathematica. Time used: 0.781 (sec). Leaf size: 105

ode=(8*x^2*y[x]^3-2*y[x]^4)+(5*x^3*y[x]^2-8*x*y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to 0 \\ \text {Solve}\left [\frac {286^{2/3} x^2 \log (x)}{\sqrt [3]{-x^6}}+60 c_1&=60 \int _1^{\frac {16 x^2 y(x)-55 x^4}{\sqrt [3]{286} \sqrt [3]{-x^6} \left (5 x^2-8 y(x)\right )}}\frac {1}{K[1]^3+\frac {147 \sqrt [3]{-1} K[1]}{286^{2/3}}+1}dK[1],y(x)\right ] \\ \end{align*}

✓ Sympy. Time used: 9.606 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x**2*y(x)**3 + (5*x**3*y(x)**2 - 8*x*y(x)**3)*Derivative(y(x), x) - 2*y(x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 0 \]