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 : Sunday, March 30, 2025 at 11:47:55 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*}

✓ Maple. Time used: 0.070 (sec). Leaf size: 27

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

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

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

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

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

✓ Sympy. Time used: 0.328 (sec). Leaf size: 22

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

\[ \left [ y{\left (x \right )} = - \sqrt {1 - x^{2}}, \ y{\left (x \right )} = \sqrt {1 - x^{2}}\right ] \]