50.6.7 problem 1(g)

Internal problem ID [7899]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page 32
Problem number : 1(g)
Date solved : Wednesday, March 05, 2025 at 05:16:55 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 41

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

\begin{align*} y &= -\frac {\sqrt {-x \left (x^{4}-4 c_{1} \right )}}{2 x^{2}} \\ y &= \frac {\sqrt {-x \left (x^{4}-4 c_{1} \right )}}{2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.239 (sec). Leaf size: 55

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

✓ Sympy. Time used: 0.434 (sec). Leaf size: 29

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

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