20.5.5 problem Problem 5

Internal problem ID [3688]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number : Problem 5
Date solved : Monday, January 27, 2025 at 07:55:24 AM
CAS classification : [_separable]

\begin{align*} 2 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

\[ y \left (x \right ) = \frac {c_{1}}{x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 20

DSolve[2*x*y[x]+(x^2+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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