81.3.19 problem 19

Internal problem ID [18566]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 19
Date solved : Monday, March 31, 2025 at 05:43:04 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 27

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

\[ \frac {x^{4}}{4}+2 x^{2} y+x y^{2}+y^{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.245 (sec). Leaf size: 1965

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

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

✗ Sympy

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

Timed Out