36.1.35 problem 31 part(b.1)

Internal problem ID [6290]
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.1)
Date solved : Monday, January 27, 2025 at 01:54:54 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 16

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

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