65.7.8 problem 12

Internal problem ID [15716]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 12
Date solved : Thursday, October 02, 2025 at 10:23:55 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=x-y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {x^{2}+c_1} \\ y &= -\sqrt {x^{2}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to -\sqrt {x^2+2 c_1}\\ y(x)&\to \sqrt {x^2+2 c_1} \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 22

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

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