7.5.39 problem 39

Internal problem ID [143]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 39
Date solved : Saturday, March 29, 2025 at 04:36:23 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

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

\begin{align*} y &= 0 \\ y^{4} x +x^{3} y^{3}+\frac {y^{5}}{5}+c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 32.434 (sec). Leaf size: 171

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

\begin{align*} y(x)\to 0 \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,5\right ] \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out