44.4.21 problem 7 (a)

Internal problem ID [7034]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 7 (a)
Date solved : Monday, January 27, 2025 at 02:41:41 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 13

dsolve([y(x)*diff(y(x),x)=-x,y(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 16

DSolve[{y[x]*D[y[x],x]==-x,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

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