32.5.7 problem Exercise 11.7, page 97

Internal problem ID [5845]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.7, page 97
Date solved : Tuesday, March 04, 2025 at 11:48:04 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\begin{align*} y \left (x \right ) &= -\frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{2 x}+4 x}} \\ y \left (x \right ) &= \frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{2 x}+4 x}} \\ \end{align*}

✓ Mathematica. Time used: 3.133 (sec). Leaf size: 50

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

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

✓ Sympy. Time used: 0.725 (sec). Leaf size: 49

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

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