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 : Monday, January 27, 2025 at 02:56:15 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

With initial conditions

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

✓ Solution by Maple

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

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

\[ y = -x \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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