71.8.33 problem 11 (d)

Internal problem ID [14388]
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 (d)
Date solved : Saturday, February 22, 2025 at 03:44:33 PM
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: 0.021 (sec). Leaf size: 15

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

\[ y = x -\sqrt {x^{2}+3} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 58

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-1}{(K[1]-2) K[1]}dK[1]=\int _1^{-1}\frac {K[1]-1}{(K[1]-2) K[1]}dK[1]-\log (x),y(x)\right ] \]

✓ Sympy. Time used: 0.918 (sec). Leaf size: 12

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)
 

\[ y{\left (x \right )} = x - \sqrt {x^{2} + 3} \]