87.5.14 problem 18

Internal problem ID [23307]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 47
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:31:15 PM
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 )&=2 \\ \end{align*}

✓ Maple. Time used: 0.275 (sec). Leaf size: 15

ode:=x+y(x)+(x-y(x))*diff(y(x),x) = 0; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x +\sqrt {2 x^{2}+4} \]

✓ Mathematica. Time used: 0.243 (sec). Leaf size: 22

ode=(x+y[x])+( x-y[x] )*D[y[x],x]==0; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.794 (sec). Leaf size: 14

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): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x + \sqrt {2 x^{2} + 4} \]