60.1.112 problem 112

Internal problem ID [10126]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 112
Date solved : Monday, January 27, 2025 at 06:28:36 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: 0.005 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.307 (sec). Leaf size: 13

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

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