81.1.42 problem 2-40

Internal problem ID [21487]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-40
Date solved : Thursday, October 02, 2025 at 07:41:46 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 882

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

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

✓ Mathematica. Time used: 60.085 (sec). Leaf size: 821

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

\begin{align*} y(x)&\to \frac {2 x^2+\frac {2 \sqrt [3]{2} x^4}{\sqrt [3]{\left (2-27 c_1{}^2\right ) x^6+54 c_1 x^5-27 (1+4 c_1) x^4+108 x^3-108 x^2+3 \sqrt {3} \sqrt {x^4 \left (c_1 x^2-x+2\right ){}^2 \left (\left (-4+27 c_1{}^2\right ) x^4-54 c_1 x^3+27 (1+4 c_1) x^2-108 x+108\right )}}}+2^{2/3} \sqrt [3]{\left (2-27 c_1{}^2\right ) x^6+54 c_1 x^5-27 (1+4 c_1) x^4+108 x^3-108 x^2+3 \sqrt {3} \sqrt {x^4 \left (c_1 x^2-x+2\right ){}^2 \left (\left (-4+27 c_1{}^2\right ) x^4-54 c_1 x^3+27 (1+4 c_1) x^2-108 x+108\right )}}}{6 \left (-c_1 x^2+x-2\right )}\\ y(x)&\to \frac {4 x^2-\frac {2 i \sqrt [3]{2} \left (\sqrt {3}-i\right ) x^4}{\sqrt [3]{\left (2-27 c_1{}^2\right ) x^6+54 c_1 x^5-27 (1+4 c_1) x^4+108 x^3-108 x^2+3 \sqrt {3} \sqrt {x^4 \left (c_1 x^2-x+2\right ){}^2 \left (\left (-4+27 c_1{}^2\right ) x^4-54 c_1 x^3+27 (1+4 c_1) x^2-108 x+108\right )}}}+i 2^{2/3} \left (\sqrt {3}+i\right ) \sqrt [3]{\left (2-27 c_1{}^2\right ) x^6+54 c_1 x^5-27 (1+4 c_1) x^4+108 x^3-108 x^2+3 \sqrt {3} \sqrt {x^4 \left (c_1 x^2-x+2\right ){}^2 \left (\left (-4+27 c_1{}^2\right ) x^4-54 c_1 x^3+27 (1+4 c_1) x^2-108 x+108\right )}}}{12 \left (-c_1 x^2+x-2\right )}\\ y(x)&\to \frac {4 x^2+\frac {2 i \sqrt [3]{2} \left (\sqrt {3}+i\right ) x^4}{\sqrt [3]{\left (2-27 c_1{}^2\right ) x^6+54 c_1 x^5-27 (1+4 c_1) x^4+108 x^3-108 x^2+3 \sqrt {3} \sqrt {x^4 \left (c_1 x^2-x+2\right ){}^2 \left (\left (-4+27 c_1{}^2\right ) x^4-54 c_1 x^3+27 (1+4 c_1) x^2-108 x+108\right )}}}-2^{2/3} \left (1+i \sqrt {3}\right ) \sqrt [3]{\left (2-27 c_1{}^2\right ) x^6+54 c_1 x^5-27 (1+4 c_1) x^4+108 x^3-108 x^2+3 \sqrt {3} \sqrt {x^4 \left (c_1 x^2-x+2\right ){}^2 \left (\left (-4+27 c_1{}^2\right ) x^4-54 c_1 x^3+27 (1+4 c_1) x^2-108 x+108\right )}}}{12 \left (-c_1 x^2+x-2\right )} \end{align*}

✗ Sympy

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

Timed Out