Internal problem ID [5227]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 2. Solutions of differential equations. Supplemetary problems. Page
11
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(y(x)*diff(y(x),x)+x=0,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: 0.078 (sec). Leaf size: 39
DSolve[y[x]*y'[x]+x==0,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*}