73.7.13 problem 13

Internal problem ID [15092]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 13
Date solved : Thursday, March 13, 2025 at 05:37:38 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

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

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

\begin{align*} y &= \frac {x}{\sqrt {2 x^{3}+c_{1}}} \\ y &= -\frac {x}{\sqrt {2 x^{3}+c_{1}}} \\ \end{align*}

✓ Mathematica. Time used: 0.207 (sec). Leaf size: 43

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

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

✓ Sympy. Time used: 0.592 (sec). Leaf size: 32

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

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