44.2.6 problem 6

Internal problem ID [6938]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:37:29 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {1}{2}\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 15

dsolve([diff(y(x),x)+2*x*y(x)^2=0,y(1/2) = -4],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 16

DSolve[{D[y[x],x]+2*x*y[x]^2==0,{y[1/2]==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2}{2 x^2-1} \]