85.4.3 problem 1 (c)

Internal problem ID [22444]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. A Exercises at page 21
Problem number : 1 (c)
Date solved : Thursday, October 02, 2025 at 08:39:33 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (-2\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.122 (sec). Leaf size: 15

ode:=diff(y(x),x) = (x+y(x))/(y(x)-x); 
ic:=[y(-2) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x +\sqrt {2 x^{2}+17} \]

✓ Mathematica. Time used: 0.254 (sec). Leaf size: 18

ode=D[y[x],{x,1}]==(y[x]+x)/(y[x]-x); 
ic={y[-2]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {2 x^2+17}+x \end{align*}

✓ Sympy. Time used: 0.729 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x + y(x))/(-x + y(x)),0) 
ics = {y(-2): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x + \sqrt {2 x^{2} + 17} \]