12.3.20 problem 21

Internal problem ID [1597]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 21
Date solved : Monday, January 27, 2025 at 05:12:59 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (3\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 15

dsolve([x+y(x)*diff(y(x),x)=0,y(3) = -4],y(x), singsol=all)
 

\[ y = -\sqrt {-x^{2}+25} \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 18

DSolve[{x+y[x]*D[y[x],x]==0,y[3]==-4},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {25-x^2} \]