12.6.28 problem 28(a)

Internal problem ID [1707]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 28(a)
Date solved : Saturday, March 29, 2025 at 11:35:19 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} x^{2}+y^{2}+2 x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 47

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

\begin{align*} y &= -\frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_1 \right )}}{3 x} \\ y &= \frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_1 \right )}}{3 x} \\ \end{align*}

✓ Mathematica. Time used: 0.206 (sec). Leaf size: 60

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

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

✓ Sympy. Time used: 0.442 (sec). Leaf size: 39

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {3} \sqrt {\frac {C_{1}}{x} - x^{2}}}{3}, \ y{\left (x \right )} = \frac {\sqrt {3} \sqrt {\frac {C_{1}}{x} - x^{2}}}{3}\right ] \]