78.5.21 problem 4 (j)

Internal problem ID [18093]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (j)
Date solved : Monday, March 31, 2025 at 05:09:50 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 31

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

\[ \ln \left (x \right )-c_1 +\frac {2 \ln \left (x^{2} y^{4}+3\right )}{3}-\frac {2 \ln \left (y \sqrt {x}\right )}{3} = 0 \]

✓ Mathematica. Time used: 60.122 (sec). Leaf size: 1141

ode=x*D[y[x],x]-y[x] == x^2*y[x]^4*(x*D[y[x],x]+y[x]); 
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**2*(x*Derivative(y(x), x) + y(x))*y(x)**4 + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out