7.3.2 problem 2

Internal problem ID [42]
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 : 2
Date solved : Friday, February 07, 2025 at 08:12:49 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+2 x y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

dsolve(diff(y(x),x)+2*x*y(x)^2=0,y(x), singsol=all)
 

\[ y = \frac {1}{x^{2}+c_1} \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 20

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

\begin{align*} y(x)\to \frac {1}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}