44.2.4 problem 4

Internal problem ID [6936]
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 : 4
Date solved : Monday, January 27, 2025 at 02:37:23 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 12

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

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