65.8.30 problem 11 (a)

Internal problem ID [15751]
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 (a)
Date solved : Thursday, October 02, 2025 at 10:26:37 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 )&=2 \\ \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 7

ode:=diff(y(x),x) = y(x)/(y(x)-x); 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 x \]

✓ Mathematica. Time used: 0.259 (sec). Leaf size: 14

ode=D[y[x],x]==y[x]/(y[x]-x); 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.634 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - y(x)/(-x + y(x)),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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