36.1.37 problem 31 part(b.3)

Internal problem ID [6292]
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.3)
Date solved : Monday, January 27, 2025 at 01:55:04 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 18

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

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