8.3.11 problem 11

Internal problem ID [687]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 11
Date solved : Tuesday, March 04, 2025 at 11:32:30 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.141 (sec). Leaf size: 44

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

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

✓ Sympy. Time used: 0.312 (sec). Leaf size: 29

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

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