44.5.65 problem 55 (b)

Internal problem ID [7127]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 55 (b)
Date solved : Tuesday, February 04, 2025 at 12:23:22 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 27

dsolve([diff(y(x),x)=-x/y(x),y(1) = 0],y(x), singsol=all)
 

\begin{align*} y &= \sqrt {-x^{2}+1} \\ y &= -\sqrt {-x^{2}+1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 33

DSolve[{D[y[x],x]==-x/y[x],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {1-x^2} \\ y(x)\to \sqrt {1-x^2} \\ \end{align*}