47.2.5 problem 5

Internal problem ID [7421]
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 : 5
Date solved : Monday, January 27, 2025 at 02:54:27 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.064 (sec). Leaf size: 47

dsolve((x^2+y(x)^2)*diff(y(x),x)=2*x*y(x),y(x), singsol=all)
 

\begin{align*} y &= \frac {1-\sqrt {4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ y &= \frac {1+\sqrt {4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.187 (sec). Leaf size: 70

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

\begin{align*} y(x)\to \frac {1}{2} \left (-\sqrt {4 x^2+e^{2 c_1}}-e^{c_1}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {4 x^2+e^{2 c_1}}-e^{c_1}\right ) \\ y(x)\to 0 \\ \end{align*}