85.33.33 problem 33

Internal problem ID [22656]
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 65
Problem number : 33
Date solved : Thursday, October 02, 2025 at 09:02:58 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

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

\begin{align*} y &= \frac {\sqrt {x \left (-x^{2}+c_1 \right )}}{x^{2}} \\ y &= -\frac {\sqrt {x \left (-x^{2}+c_1 \right )}}{x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 46

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

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

✓ Sympy. Time used: 0.301 (sec). Leaf size: 29

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

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