77.7.6 problem 4 (b)

Internal problem ID [20409]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (F) at page 24
Problem number : 4 (b)
Date solved : Thursday, October 02, 2025 at 05:53:04 PM
CAS classification : [_rational]

\begin{align*} \left (20 x^{2}+8 y x +4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+y x +y^{2}+y^{3}\right ) x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 38

ode:=(20*x^2+8*x*y(x)+4*y(x)^2+3*y(x)^3)*y(x)+4*(x^2+x*y(x)+y(x)^2+y(x)^3)*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ 4 x^{5} y+2 x^{4} y^{2}+\frac {4 x^{3} y^{3}}{3}+x^{3} y^{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.159 (sec). Leaf size: 2173

ode=(20*x^2+8*x*y[x]+4*y[x]^2+3*y[x]^3)*y[x]+4*(x^2+x*y[x]+y[x]^2+y[x]^3)*x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(4*x**2 + 4*x*y(x) + 4*y(x)**3 + 4*y(x)**2)*Derivative(y(x), x) + (20*x**2 + 8*x*y(x) + 3*y(x)**3 + 4*y(x)**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out