31.1.9 problem 3.3

Internal problem ID [5707]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 3.3
Date solved : Monday, January 27, 2025 at 01:10:44 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.300 (sec). Leaf size: 13

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

\[ y(x)\to x \sinh (\log (x)+c_1) \]