84.14.4 problem 7.12

Internal problem ID [22161]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Supplementary problems
Problem number : 7.12
Date solved : Thursday, October 02, 2025 at 08:33:02 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.305 (sec). Leaf size: 44

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

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

✓ Sympy. Time used: 0.327 (sec). Leaf size: 29

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

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