89.10.11 problem 11

Internal problem ID [24504]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:43:43 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

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

\begin{align*} y &= \frac {1}{\sqrt {x \left (c_1 x +2\right )}\, x} \\ y &= -\frac {1}{\sqrt {x \left (c_1 x +2\right )}\, x} \\ \end{align*}

✓ Mathematica. Time used: 0.357 (sec). Leaf size: 44

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

\begin{align*} y(x)&\to -\frac {1}{\sqrt {x^3 (2+c_1 x)}}\\ y(x)&\to \frac {1}{\sqrt {x^3 (2+c_1 x)}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.556 (sec). Leaf size: 32

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

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