7.3.11 problem 11

Internal problem ID [51]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 11
Date solved : Friday, February 07, 2025 at 07:46:59 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (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: 0.144 (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*}