38.4.21 problem 7 (a)

Internal problem ID [8320]
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 : Tuesday, September 30, 2025 at 05:26:20 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 13

ode:=y(x)*diff(y(x),x) = -x; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.220 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + y(x)*Derivative(y(x), x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {2 - x^{2}} \]