32.6.18 problem Exercise 12.18, page 103

Internal problem ID [5883]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.18, page 103
Date solved : Sunday, March 30, 2025 at 10:22:45 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+8 x^{3} y^{3}+2 x y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 43

ode:=diff(y(x),x)+8*x^3*y(x)^3+2*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{2 x^{2}} c_1 -4 x^{2}-2}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{2 x^{2}} c_1 -4 x^{2}-2}} \\ \end{align*}

✓ Mathematica. Time used: 7.443 (sec). Leaf size: 58

ode=D[y[x],x]+8*x^3*y[x]^3+2*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {-4 x^2+c_1 e^{2 x^2}-2}} \\ y(x)\to \frac {1}{\sqrt {-4 x^2+c_1 e^{2 x^2}-2}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.712 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x**3*y(x)**3 + 2*x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {- \frac {1}{C_{1} e^{2 x^{2}} + 4 x^{2} + 2}}, \ y{\left (x \right )} = \sqrt {- \frac {1}{C_{1} e^{2 x^{2}} + 4 x^{2} + 2}}\right ] \]