36.1.34 problem 31 part(a)

Internal problem ID [6289]
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(a)
Date solved : Monday, January 27, 2025 at 01:54:52 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 44

DSolve[D[y[x],x]==x*y[x]^3,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*}