Internal problem ID [13746]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\frac {x}{y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x)=-x/y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {-x^{2}+c_{1}} y \left (x \right ) = -\sqrt {-x^{2}+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.201 (sec). Leaf size: 39
DSolve[y'[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*}