8.3.2 problem 2

Internal problem ID [678]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:57:33 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 20

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

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