47.2.13 problem 13

Internal problem ID [7429]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 13
Date solved : Wednesday, March 05, 2025 at 04:32:25 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.105 (sec). Leaf size: 7

ode:=x^2+2*x*y(x)-y(x)^2+(y(x)^2+2*x*y(x)-x^2)*diff(y(x),x) = 0; 
ic:=y(1) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -x \]

✗ Mathematica

ode=(x^2+2*x*y[x]-y[x]^2)+(y[x]^2+2*x*y[x]-x^2)*D[y[x],x]==0; 
ic={y[1]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

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