74.1.22 problem 29

Internal problem ID [15802]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 08:07:41 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-\frac {x}{y} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(diff(y(x),x)=-x/y(x),y(x), singsol=all)
 

\begin{align*} y &= \sqrt {-x^{2}+c_{1}} \\ y &= -\sqrt {-x^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 39

DSolve[D[y[x],x]==-x/y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-x^2+2 c_1} \\ y(x)\to \sqrt {-x^2+2 c_1} \\ \end{align*}