44.5.6 problem 6

Internal problem ID [7068]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:46:43 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.106 (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*}