47.2.11 problem 11

Internal problem ID [7427]
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 : 11
Date solved : Monday, January 27, 2025 at 02:55:03 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(x*diff(y(x),x)-sqrt(x^2-y(x)^2)-y(x)=0,y(x), singsol=all)
 

\[ -\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )+\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.252 (sec). Leaf size: 18

DSolve[x*D[y[x],x]-Sqrt[x^2-y[x]^2]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \cosh (i \log (x)+c_1) \]