40.1.2 problem 14

Internal problem ID [6570]
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
Date solved : Monday, January 27, 2025 at 02:12:26 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (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: 0.089 (sec). Leaf size: 39

DSolve[y[x]*D[y[x],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*}