Internal problem ID [7695]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 114.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime } x -y-x \sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.654 (sec). Leaf size: 28
dsolve(x*diff(y(x),x) - x*sqrt(y(x)^2 + x^2) - y(x)=0,y(x), singsol=all)
\[ \ln \left (\sqrt {x^{2}+y \relax (x )^{2}}+y \relax (x )\right )-x -\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 46.492 (sec). Leaf size: 46
DSolve[x*y'[x] - x*Sqrt[y[x]^2 + x^2] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \tanh (x+c_1)}{\sqrt {\operatorname {sech}^2(x+c_1)}} \\ y(x)\to \frac {x \tanh (x+c_1)}{\sqrt {\operatorname {sech}^2(x+c_1)}} \\ \end{align*}