83.4.1 problem 1 (a)

Internal problem ID [21928]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. V at page 42
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 08:13:21 PM
CAS classification : [_exact, _rational]

\begin{align*} 2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

ode:=2*x^2+5*x*y(x)^2+(5*x^2*y(x)-2*y(x)^4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 2.963 (sec). Leaf size: 161

ode=(2*x^2+5*x*y[x]^2)+(5*x^2*y[x]-2*y[x]^4)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [12 \text {$\#$1}^5-75 \text {$\#$1}^2 x^2-20 x^3-30 c_1\&,1\right ]\\ y(x)&\to \text {Root}\left [12 \text {$\#$1}^5-75 \text {$\#$1}^2 x^2-20 x^3-30 c_1\&,2\right ]\\ y(x)&\to \text {Root}\left [12 \text {$\#$1}^5-75 \text {$\#$1}^2 x^2-20 x^3-30 c_1\&,3\right ]\\ y(x)&\to \text {Root}\left [12 \text {$\#$1}^5-75 \text {$\#$1}^2 x^2-20 x^3-30 c_1\&,4\right ]\\ y(x)&\to \text {Root}\left [12 \text {$\#$1}^5-75 \text {$\#$1}^2 x^2-20 x^3-30 c_1\&,5\right ] \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2 + 5*x*y(x)**2 + (5*x**2*y(x) - 2*y(x)**4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out