Internal problem ID [7693]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 112.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-\sqrt {y^{2}+x^{2}}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 27
dsolve(x*diff(y(x),x) - sqrt(y(x)^2 + x^2) - y(x)=0,y(x), singsol=all)
\[ \frac {\sqrt {x^{2}+y \relax (x )^{2}}}{x^{2}}+\frac {y \relax (x )}{x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 7.886 (sec). Leaf size: 50
DSolve[x*y'[x] - Sqrt[y[x]^2 + x^2] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \tanh (\log (x)+c_1)}{\sqrt {\operatorname {sech}^2(\log (x)+c_1)}} \\ y(x)\to \frac {x \tanh (\log (x)+c_1)}{\sqrt {\operatorname {sech}^2(\log (x)+c_1)}} \\ \end{align*}