21.1.2 problem 2

Internal problem ID [4296]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.1
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 07:13:57 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.060 (sec). Leaf size: 22

ode:=x+y(x)+(x-y(x))*diff(y(x),x) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\begin{align*} y &= \left (1+\sqrt {2}\right ) x \\ y &= -\left (\sqrt {2}-1\right ) x \\ \end{align*}

✓ Mathematica. Time used: 0.249 (sec). Leaf size: 40

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

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

✓ Sympy. Time used: 0.729 (sec). Leaf size: 31

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

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