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 : Monday, January 27, 2025 at 01:54:59 PM
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*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

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

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

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