65.8.31 problem 11 (b)

Internal problem ID [15752]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 11 (b)
Date solved : Thursday, October 02, 2025 at 10:26:41 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 33

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

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

✓ Sympy. Time used: 0.628 (sec). Leaf size: 24

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

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