64.6.9 problem 9

Internal problem ID [13280]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 9
Date solved : Wednesday, March 05, 2025 at 09:33:16 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \end{align*}

✓ Maple. Time used: 0.186 (sec). Leaf size: 41

ode:=diff(y(x),x) = (4*x^3*y(x)^2-3*x^2*y(x))/(x^3-2*x^4*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {x -\sqrt {x^{2}+4 c_{1}}}{2 x^{2}} \\ y &= \frac {x +\sqrt {x^{2}+4 c_{1}}}{2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.76 (sec). Leaf size: 78

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

\begin{align*} y(x)\to \frac {x^3-\sqrt {x^2} \sqrt {x^4+4 c_1 x^2}}{2 x^4} \\ y(x)\to \frac {x^3+\sqrt {x^2} \sqrt {x^4+4 c_1 x^2}}{2 x^4} \\ \end{align*}

✓ Sympy. Time used: 1.042 (sec). Leaf size: 34

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

\[ \left [ y{\left (x \right )} = \frac {1 - \sqrt {\frac {C_{1}}{x^{2}} + 1}}{2 x}, \ y{\left (x \right )} = \frac {\sqrt {\frac {C_{1}}{x^{2}} + 1} + 1}{2 x}\right ] \]