Internal problem ID [8451]
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)]`]]
\[ \boxed {y^{\prime } x -x \sqrt {x^{2}+y^{2}}-y=0} \]
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 28
dsolve(x*diff(y(x),x) - x*sqrt(y(x)^2 + x^2) - y(x)=0,y(x), singsol=all)
\[ \ln \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )-x -\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 30
DSolve[x*y'[x] - x*Sqrt[y[x]^2 + x^2] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x e^{-x-c_1} \left (-1+e^{2 (x+c_1)}\right ) \]