85.18.1 problem 1 (a)

Internal problem ID [22547]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 52
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 08:49:42 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=3*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 {-x^{3}+c_1}}{x} \\ y &= -\frac {\sqrt {-x^{3}+c_1}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 42

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

✓ Sympy. Time used: 0.227 (sec). Leaf size: 26

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

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