36.1.36 problem 31 part(b.2)

Internal problem ID [6291]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 31 part(b.2)
Date solved : Sunday, March 30, 2025 at 10:49:33 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Maple. Time used: 0.124 (sec). Leaf size: 13

ode:=diff(y(x),x) = x*y(x)^3; 
ic:=y(0) = 1/2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {1}{\sqrt {-x^{2}+4}} \]

✓ Mathematica. Time used: 0.103 (sec). Leaf size: 16

ode=D[y[x],x]==x*y[x]^3; 
ic={y[0]==1/2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{\sqrt {4-x^2}} \]

✓ Sympy. Time used: 0.370 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**3 + Derivative(y(x), x),0) 
ics = {y(0): 1/2} 
dsolve(ode,func=y(x),ics=ics)
 

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