85.25.2 problem 2

Internal problem ID [22587]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 57
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:53:38 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 25

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

\[ -\frac {x^{2}}{2}-\frac {1}{3 x^{3} y^{3}}-\frac {y^{2}}{2}+c_1 = 0 \]

✓ Mathematica. Time used: 2.414 (sec). Leaf size: 181

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

\begin{align*} y(x)&\to \text {Root}\left [3 \text {$\#$1}^5 x^3+\text {$\#$1}^3 \left (3 x^5-6 c_1 x^3\right )+2\&,1\right ]\\ y(x)&\to \text {Root}\left [3 \text {$\#$1}^5 x^3+\text {$\#$1}^3 \left (3 x^5-6 c_1 x^3\right )+2\&,2\right ]\\ y(x)&\to \text {Root}\left [3 \text {$\#$1}^5 x^3+\text {$\#$1}^3 \left (3 x^5-6 c_1 x^3\right )+2\&,3\right ]\\ y(x)&\to \text {Root}\left [3 \text {$\#$1}^5 x^3+\text {$\#$1}^3 \left (3 x^5-6 c_1 x^3\right )+2\&,4\right ]\\ y(x)&\to \text {Root}\left [3 \text {$\#$1}^5 x^3+\text {$\#$1}^3 \left (3 x^5-6 c_1 x^3\right )+2\&,5\right ] \end{align*}

✗ Sympy

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

Timed Out