31.2.2 problem 2

Internal problem ID [5723]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:11:36 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} 1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 38

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

\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+c_1} \\ y(x)\to \sqrt {x} \sqrt {x+c_1} \\ \end{align*}