77.7.2 problem 2 (a)

Internal problem ID [20405]
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 : 2 (a)
Date solved : Thursday, October 02, 2025 at 05:52:55 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 38

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

\begin{align*} y &= 0 \\ y &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-4 \ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+4 c_1 \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2\right )}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.21 (sec). Leaf size: 40

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

\begin{align*} y(x)&\to 0\\ \text {Solve}\left [\frac {1}{2} x^2 y(x)^2-\frac {1}{x y(x)}-\log (y(x))+\log (x)=c_1,y(x)\right ] \end{align*}

✓ Sympy. Time used: 2.008 (sec). Leaf size: 34

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

\[ \left [ - \frac {x^{2} y^{2}{\left (x \right )}}{4} - \log {\left (x \right )} + \frac {\log {\left (x y{\left (x \right )} \right )}}{2} + \frac {1}{2 x y{\left (x \right )}} = C_{1}, \ y{\left (x \right )} = 0\right ] \]