8.5.34 problem 34

Internal problem ID [762]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 34
Date solved : Saturday, March 29, 2025 at 10:20:23 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 117

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

\begin{align*} y &= -\frac {\sqrt {-2 x^{2}-2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ y &= \frac {\sqrt {-2 x^{2}-2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ y &= -\frac {\sqrt {-2 x^{2}+2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ y &= \frac {\sqrt {-2 x^{2}+2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ \end{align*}

✓ Mathematica. Time used: 5.977 (sec). Leaf size: 155

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

\begin{align*} y(x)\to -\frac {\sqrt {-x^2-\sqrt {x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-x^2-\sqrt {x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-x^2+\sqrt {x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-x^2+\sqrt {x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ \end{align*}

✗ Sympy

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

Timed Out