43.22.1 problem 1(a)

Internal problem ID [9033]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 198
Problem number : 1(a)
Date solved : Tuesday, September 30, 2025 at 06:02:17 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 185

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

\begin{align*} y &= \frac {-12 c_1 \,x^{2}+\left (108+12 \sqrt {12 x^{6} c_1^{3}+81}\right )^{{2}/{3}}}{6 \left (108+12 \sqrt {12 x^{6} c_1^{3}+81}\right )^{{1}/{3}} \sqrt {c_1}} \\ y &= -\frac {\left (1+i \sqrt {3}\right ) \left (108+12 \sqrt {12 x^{6} c_1^{3}+81}\right )^{{1}/{3}}}{12 \sqrt {c_1}}-\frac {\sqrt {c_1}\, x^{2} \left (i \sqrt {3}-1\right )}{\left (108+12 \sqrt {12 x^{6} c_1^{3}+81}\right )^{{1}/{3}}} \\ y &= \frac {\left (i \sqrt {3}-1\right ) \left (108+12 \sqrt {12 x^{6} c_1^{3}+81}\right )^{{1}/{3}}}{12 \sqrt {c_1}}+\frac {\sqrt {c_1}\, x^{2} \left (1+i \sqrt {3}\right )}{\left (108+12 \sqrt {12 x^{6} c_1^{3}+81}\right )^{{1}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 44

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {3 K[1]^2+1}{K[1] \left (K[1]^2+1\right )}dK[1]=-3 \log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out